檢視一元三次方程式的原始碼

[[分類:數學]]
<table class=nicetable>
<tr><th>n</th><th>1,n,-(n+1)</th><th>x<sup>3</sup>-3px+q=0</th><th>uv=p,u<sup>3</sup>+v<sup>3</sup>=-q</th><th><math>w^2+n(n+1)w+[\frac{n(n+1)+1}{3}]^3=0</math></th><th colspan=2>

<math>w=\frac{-n(n+1)}{2} \pm \sqrt{[\frac{n(n+1)}{2}]^2-\frac{[n(n+1)+1]^3}{3^3}}</math>

</th><th>u,v=<math>\frac{n}{2}</math>±<math>\frac{n+2}{2\sqrt{3}}i</math></th></tr>

<tr><th>n=-1</th><th>1,-1,0</th><th>x<sup>3</sup>-x=0</th><th>uv=1/3,u<sup>3</sup>+v<sup>3</sup>=0</th><th>w<sup>2</sup>+<math>\frac{1}{27}</math>=0</th><th>w=±<math>\frac{1}{3\sqrt{3}}</math>i</th><th>u,v=±<math>\frac{1}{\sqrt{3}}</math>i</th><th></th></tr>
<tr><th>n=0 </th><th>1,0,-1</th><th>x<sup>3</sup>-x=0</th><th>uv=1/3,u<sup>3</sup>+v<sup>3</sup>=0</th><th>w<sup>2</sup>+<math>\frac{1}{27}</math>=0</th><th>w=±<math>\frac{1}{3\sqrt{3}}</math>i</th><th>u,v=±<math>\frac{1}{\sqrt{3}}</math>i</th><th>u,v=<math>\frac{0}{2}</math>±<math>\frac{0+2}{2\sqrt{3}}i</math></th></tr>



</table>