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Linear Equation in One Variable

solve the equ...

Question

solve the equation
$\sqrt{(2 x + 5)} + \sqrt{(5 x + 6)} = \sqrt{(12 x + 25)}$

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Solution

$\sqrt{(2 x + 5)} + \sqrt{(5 x + 6)} = \sqrt{(12 x + 25)}$
Squaring on both sides: $2 x + 5 + 5 x + 6 + 2 \sqrt{(2 x + 5)} \sqrt{(5 x + 6)} = 12 x + 25$
$\Rightarrow 2 \sqrt{(2 x + 5)} \sqrt{(5 x + 6)} = 5 x + 14$
$\Rightarrow 4 (2 x + 5) (5 x + 6) = 25 x^{2} + 196 + 140 x$
$\Rightarrow 15 x^{2} + 8 x - 76 = 0$
Therefore, $x = 2$

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