令\(x=\sqrt[4]{5}\)
\(\begin{array}{*{35}{l}}
\begin{align}
& \\
& {{x}^{5}}=5x \\
\end{align} \\
{{x}^{5}}-5x=\left( {{x}^{3}}+2{{x}^{2}}+3x+4 \right)\left( {{x}^{2}}-2x+1 \right)-4=0 \\
\left( {{x}^{3}}+2{{x}^{2}}+3x+4 \right)\left( {{x}^{2}}-2x+1 \right)=4 \\
{} \\
\frac{2}{\sqrt{\sqrt[4]{125}+2\sqrt[4]{25}+3\sqrt[4]{5}+4}} \\
\begin{align}
& \\
& =\frac{2}{\sqrt{{{x}^{3}}+2{{x}^{2}}+3x+4}} \\
\end{align} \\
\begin{align}
& \\
& =\frac{2}{\sqrt{\frac{4}{\left( {{x}^{2}}-2x+1 \right)}}} \\
\end{align} \\
\begin{align}
& \\
& =x-1 \\
\end{align} \\
\begin{align}
& \\
& =\sqrt[4]{5}-1 \\
\end{align} \\
\end{array}\)
[ 本帖最後由 thepiano 於 2014-7-1 02:24 PM 編輯 ]
