Answer
$x=-2.78$, $-0.51$, $0.51$ and $2.78$
Work Step by Step
Given equation-
$x^{4} - 8 x^{2}+2$ = $0$
We are asked to find all real solutions of this equation.
Graphing y= $x^{4} - 8 x^{2}+2$, using graphing calculator-
We get four x−intercepts, i.e. $x=-2.7824$, $x=-0.50827$, $x=0.50827$ and $x=2.7824$
Therefore $x=-2.78$, $-0.51$, $0.51$ and $2.78$
(Rounded to two decimals)