Solve the following equation;
$x^{4} - 10 x^{2} + 9 = 0$

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Solution

$x^{4} - 10 x^{2} + 9 = 0$
$x^{4} - 9 x^{2} - x^{2} + 9 = 0$
$x^{2} (x^{2} - 9) - 1 (x^{2} - 9) = 0$
$(x^{2} - 9) (x^{2} - 1) = 0$
Now, $x^{2} - 9 = 0 x = \pm 3$ or $x^{2} - 1 = 0 x = \pm 1$

So, $x = - 3, + 3, - 1, + 1$

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