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Factors of Algebraic Expressions and Factorisation

Solve the fol...

Question

Solve the following:
$2 - \sqrt{1 - x^{2}} \sqrt{4 - x^{2}} = 0$

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Solution

$2 - \sqrt{1 - x^{2}} \sqrt{4 - x^{2}} = 0$

$0 = 2 - \sqrt{x^{4} - 5 x^{2} + 4}$

$2 = \sqrt{x^{4} - 5 x^{2} + 4}$

$4 = x^{4} - 5 x^{2} + 4$

$x^{4} - 5 x^{2} = 0$

$x^{2} = 5 : x = \sqrt{5}, x = - \sqrt{5}$

$x = \sqrt{5}, x = - \sqrt{5}, x = 0$

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