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Solve the fol...

Question

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

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Solution

$\sqrt{1 + 4 x - x^{2}} = x - 1 1 + 4 x - x^{2} = {(x - 1)}^{2} 1 + 4 x - x^{2} = x^{2} - 2 x + 1 2 x^{2} - 6 x = 0 x^{2} - 3 x = 0 x (x - 3) = 0 x = 0, 3$

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