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Functions

Solve: √ 9+...

Question

Solve: $\sqrt{9 + 2 x} - \sqrt{2 x} = \frac{5}{\sqrt{9 + 2 x}}$

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Solution

$\sqrt{9 + 2 x} - \sqrt{2 x} = \frac{5}{\sqrt{9 + 2 x}}$
$\Rightarrow x \geq 0$ & $x \geq - 9 / 2$
$\Rightarrow 9 + 2 x - \sqrt{(9 + 2 x) 2 x} = 5$
$\Rightarrow 2 x + 4 = \sqrt{(9 + 2 x) 2 x}$
Squaring
$\Rightarrow 4 x^{2} + 16 x + 16 = (9 + 2 x) 2 x$
$\Rightarrow 4 x^{2} + 16 x + 16 = 4 x^{2} + 18 x$
$\Rightarrow x = 8$

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