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Integration by Substitution

Solve the fol...

Question

Solve the following equation:
$\sqrt{x + 1} - 1 = \sqrt{x - \sqrt{x + 8}}$

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Solution

Squaring on both sides
$x + 1 + 1 - 2 \sqrt{(} x + 1) = x - \sqrt{(} x + 8)$
$2 (\sqrt{(} x + 1) - 1) = \sqrt{(} x + 8)$
squaring on both sides
$4 x + 8 - 8 \sqrt{(} x + 1) = x + 8$
$⟹ 3 x = 8 \sqrt{(} x + 1)$
squaring on both sides
$9 x^{2} - 64 x - 64 = 0$
$x = 8, - 0.88$

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