Question
Solve : $x^4 - 10x^2 +9 =0$
✓
Answer
$x^4 - 10x^2 +9 =0$
$\Rightarrow x^4 - 9x^2 - x^2 + 9 = 0$
$\Rightarrow x^2(x^2 - 9) -1(x^2 - 9) = 0$
$\Rightarrow (x^2 - 9)(x^2 - 1) = 0$
if $x^2 - 9 = 0$ or$ x^2 - 1 = 0$
$\Rightarrow x^2 = 9$ or $x^2 = 1$
$\Rightarrow x = ± 3$ or $x = ± 1$
$\Rightarrow x^4 - 9x^2 - x^2 + 9 = 0$
$\Rightarrow x^2(x^2 - 9) -1(x^2 - 9) = 0$
$\Rightarrow (x^2 - 9)(x^2 - 1) = 0$
if $x^2 - 9 = 0$ or$ x^2 - 1 = 0$
$\Rightarrow x^2 = 9$ or $x^2 = 1$
$\Rightarrow x = ± 3$ or $x = ± 1$
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