Calculate: x^4-10x^2+9=0

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Expression: ${x}^{4}-10{x}^{2}+9=0$

Transform the biquadratic equation into a quadratic equation by substituting $t$ for ${x}^{2}$

${t}^{2}-10t+9=0$

Solve the equation for $t$

$\begin{array} { l }t=1,\\t=9\end{array}$

Substitute back $t={x}^{2}$

$\begin{array} { l }{x}^{2}=1,\\{x}^{2}=9\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-1,\\x=1,\\{x}^{2}=9\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-1,\\x=1,\\x=-3,\\x=3\end{array}$

The equation has $4$ solutions

$\begin{array} { l }x_1=-3,& x_2=-1,& x_3=1,& x_4=3\end{array}$

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