Factorise: $x^{2} + x^{4} = 90$

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Solution

$x^{2} + x^{4} = 90$

$\Rightarrow x^{4} + x^{2} - 90 = 0$

$\Rightarrow x^{4} + 10 x^{2} - 9 x^{2} - 90 = 0$

$\Rightarrow x^{2} (x^{2} + 10) - 9 (x^{2} + 10) = 0$

$\Rightarrow (x^{2} + 10) (x^{2} - 9) = 0$

$\Rightarrow (x^{2} + 10) (x - 3) (x + 3) = 0$

$∴$ the factors are $(x^{2} + 10) (x - 3) (x + 3)$

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