http://well-being-ng.net/alWiki/index.php?action=history&feed=atom&title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F
一元三次方程式 - 修訂歷史
2026-05-06T16:01:25Z
本 Wiki 上此頁面的修訂歷史
MediaWiki 1.35.1
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8761&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-24T23:53:15Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月24日 (一) 23:53 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l63" >行 63：</td>
<td colspan="2" class="diff-lineno">行 63：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><th><math>a,b 為實數</math></th><th><math>\begin{cases} u=a+bi \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><th><math>a,b 為實數</math></th><th><math>\begin{cases} u=a+bi \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>v=a-bi \end{cases} <del class="diffchange diffchange-inline">=> </del></math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>v=a-bi \end{cases} <ins class="diffchange diffchange-inline">\Rightarrow </ins></math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8760&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-24T23:50:47Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月24日 (一) 23:50 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math>a,b 為實數 u=a+bi <del class="diffchange diffchange-inline">, </del>v=a-bi => </math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><th><math>a,b 為實數<ins class="diffchange diffchange-inline"></math></th><th><math>\begin{cases} </ins>u=a+bi <ins class="diffchange diffchange-inline">\\</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>v=a-bi <ins class="diffchange diffchange-inline">\end{cases} </ins>=> </math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8759&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-24T23:44:46Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月24日 (一) 23:44 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math>a,b 為實數 u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math>a,b 為實數 u=a+bi , v=a-bi <ins class="diffchange diffchange-inline">=> </ins></math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8755&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-23T04:35:12Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 04:35 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.若 <math>Z_1,Z_2</math> 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math><ins class="diffchange diffchange-inline">a,b 為實數 </ins>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8754&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-23T04:34:14Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 04:34 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.若 Z_1,Z_2 非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.若 <ins class="diffchange diffchange-inline"><math></ins>Z_1,Z_2<ins class="diffchange diffchange-inline"></math> </ins>非為實數則必為共軛複數，則 u,v 亦為共軛複數<table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8753&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-23T04:33:19Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 04:33 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.若 Z_1,Z_2 <del class="diffchange diffchange-inline">為共軛複數，則 </del>u,v 亦為共軛複數<table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.若 Z_1,Z_2 <ins class="diffchange diffchange-inline">非為實數則必為共軛複數，則 </ins>u,v 亦為共軛複數<table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8752&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-23T03:09:07Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 03:09 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.若 u,v <del class="diffchange diffchange-inline">為共軛複數</del><table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.若 <ins class="diffchange diffchange-inline">Z_1,Z_2 為共軛複數，則 </ins>u,v <ins class="diffchange diffchange-inline">亦為共軛複數</ins><table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8751&oldid=prev
丁志仁：/* 階段三：以二次方程式之兩根求三次方程式之三根 */
2025-11-23T03:05:30Z
<p><span dir="auto"><span class="autocomment">階段三：以二次方程式之兩根求三次方程式之三根</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 03:05 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61" >行 61：</td>
<td colspan="2" class="diff-lineno">行 61：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{cases}</math></th></tr></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>7.<table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>7.<ins class="diffchange diffchange-inline">若 u,v 為共軛複數</ins><table><tr><th><math>u=a+bi , v=a-bi</math></th><th><math>\begin{cases}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_1=u + v=2a \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>x_2=u \omega + v \omega^2=-a-\sqrt3b \\</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8750&oldid=prev
丁志仁：/* 參法法的另一種推理思路 */
2025-11-23T03:02:58Z
<p><span dir="auto"><span class="autocomment">參法法的另一種推理思路</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 03:02 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l115" >行 115：</td>
<td colspan="2" class="diff-lineno">行 115：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 按參數法結論：u,v 為 <math>\frac{n}{2}</math>±<math>\frac{n+2}{2\sqrt{3}}i</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 按參數法結論：u,v 為 <math>\frac{n}{2}</math>±<math>\frac{n+2}{2\sqrt{3}}i</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 按 u,v 為共軛複數 a±bi 則三根為 <math>2a,-a+\sqrt3b,-a-\sqrt3b</math> (卡爾單法的第 7 點)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 按 u,v 為共軛複數 a±bi 則三根為 <math>2a,-a+\sqrt3b,-a-\sqrt3b</math> (卡爾單法的第 7 點)</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># 則依第一點：<math>2a=n, -a+\<del class="diffchange diffchange-inline">sqrt3bi</del>=1, -a-\<del class="diffchange diffchange-inline">sqrt3bi</del>=-(n+1)</math>，此關係恆成立</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># 則依第一點：<math>2a=n, -a+\<ins class="diffchange diffchange-inline">sqrt3b</ins>=1, -a-\<ins class="diffchange diffchange-inline">sqrt3b</ins>=-(n+1)</math>，此關係恆成立</div></td></tr>
</table>
丁志仁
http://well-being-ng.net/alWiki/index.php?title=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F&diff=8749&oldid=prev
丁志仁：/* 參法法的另一種推理思路 */
2025-11-23T03:01:56Z
<p><span dir="auto"><span class="autocomment">參法法的另一種推理思路</span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="zh-Hant-TW">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上個修訂</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">於 2025年11月23日 (日) 03:01 的修訂</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l114" >行 114：</td>
<td colspan="2" class="diff-lineno">行 114：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===參法法的另一種推理思路===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===參法法的另一種推理思路===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 按參數法結論：u,v 為 <math>\frac{n}{2}</math>±<math>\frac{n+2}{2\sqrt{3}}i</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 按參數法結論：u,v 為 <math>\frac{n}{2}</math>±<math>\frac{n+2}{2\sqrt{3}}i</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># 按 u,v 為共軛複數 a±bi 則三根為 <math>2a,-a+\<del class="diffchange diffchange-inline">sqrt3bi</del>,-a-\<del class="diffchange diffchange-inline">sqrt3bi</del></math> (<del class="diffchange diffchange-inline">待寫段落來說明</del>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># 按 u,v 為共軛複數 a±bi 則三根為 <math>2a,-a+\<ins class="diffchange diffchange-inline">sqrt3b</ins>,-a-\<ins class="diffchange diffchange-inline">sqrt3b</ins></math> (<ins class="diffchange diffchange-inline">卡爾單法的第 7 點</ins>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 則依第一點：<math>2a=n, -a+\sqrt3bi=1, -a-\sqrt3bi=-(n+1)</math>，此關係恆成立</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># 則依第一點：<math>2a=n, -a+\sqrt3bi=1, -a-\sqrt3bi=-(n+1)</math>，此關係恆成立</div></td></tr>
</table>
丁志仁