Answer
$\left\{-3,-1,1,3\right\}$
Work Step by Step
Using factoring of trinomials, the given equation, $
x^4-10x^2+9=0
,$ is equivalent to
\begin{align*}
(x^2-9)(x^2-1)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
x^2-9=0 & x^2-1=0
\\
x^2=9 & x^2=1
.\end{array}
Taking the square root of both sides (Square Root Property), the equations above are equivalent to
\begin{array}{l|r}
x=\pm\sqrt{9} & x=\sqrt{1}
\\
x=\pm3 & x=1
.\end{array}
Hence, the solution set of the equation $
x^4-10x^2+9=0
$ is $\left\{-3,-1,1,3\right\}$.
