x 5 + p x 4 + q = 0 {\displaystyle x^{5}+px^{4}+q=0} 必然存在李煌解形式:
x = − q p y 4 {\displaystyle x={\sqrt[{^{^{4}}}]{\frac {-q}{py}}}} 其中y滿足方程: y 5 − 4 y 4 + 6 y 3 − 4 y 2 + y + q p 5 = 0 {\displaystyle y^{5}-4y^{4}+6y^{3}-4y^{2}+y+{\frac {q}{p^{5}}}=0}
x 5 + p x = q {\displaystyle x^{5}+px=q} 必然存在李煌解形式:
x = y q {\displaystyle x={\sqrt {y{\sqrt {q}}}}} 其中y滿足代數方程: y 5 + ( 2 p q ) y 3 + ( p 2 q 2 ) y = q q {\displaystyle y^{5}+({\frac {2p}{q}})y^{3}+({\frac {p^{2}}{q^{2}}})y={\frac {\sqrt {q}}{q}}}
x 5 + 3 p q x 4 + 3 p 2 q 2 x 3 + p 3 q 3 x 2 = 1 q 2 {\displaystyle x^{5}+{\frac {3p}{q}}x^{4}+{\frac {3p^{2}}{q^{2}}}x^{3}+{\frac {p^{3}}{q^{3}}}x^{2}={\frac {1}{q^{2}}}} 必然存在李煌解形式:
x = y 3 q {\displaystyle x={\frac {y^{3}}{q}}} 其中y滿足代數方程: y 5 + p y 2 = q {\displaystyle y^{5}+py^{2}=q}
<<School:李煌數學研究院
![{\displaystyle x={\sqrt[{^{^{4}}}]{\frac {-q}{py}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d23380fa90d42fe361393f1ede778a3040e03cb)
