If $(2 x + 3)^{2} + (2 x - 3)^{2} = (8 x + 6) (x - 1) + 22$ , then the value of ' $x$ '

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Solution

The correct option is C - 1
We have,
$(2 x + 3)^{2} + (2 x - 3)^{2} = (8 x + 6) (x - 1) + 22$
$[∵ (a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2})]$
$\Rightarrow 2 {(2 x)^{2} + 3^{2}} = x (8 x + 6) - (8 x + 6) + 22$
$\Rightarrow 2 (4 x^{2} + 9) = 8 x^{2} + 6 x - 8 x - 6 + 22$
$\Rightarrow 8 x^{2} + 18 = 8 x^{2} - 2 x + 16$
$\Rightarrow 8 x^{2} - 8 x^{2} + 2 x = 16 - 18$
$\Rightarrow 2 x = - 2$
$\Rightarrow x = - 1$

Hence, $x = - 1$ is the solution of the given equation.

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