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Range of Quadratic Expression

Solve the fol...

Question

Solve the following equation: $(\sqrt{2 x + 3} + \sqrt{3 x + 3}) = 1$

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Solution

$\sqrt{2 x + 3} + \sqrt{3 x + 3} = 1$
$\sqrt{2 x + 3} = 1 - \sqrt{3 x + 3}$
Squaring on both sides
$2 x + 3 = 1 + 3 x + 3 - 2 \sqrt{3 x + 3}$
$- x - 1 = 2 \sqrt{3 x + 3}$
$(x + 1)^{2} = 12 x + 12$
$x^{2} - 10 x - 11 = 0 ⟹ x = 11, - 1$

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