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

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Solution

The correct option is C - 1
We have,
$(2 x + 3)^{2} + (2 x - 3)^{2} = (8 x + 6) (x - 1) + 22 [U s i n g : (a + b)^{2} + (a - b)^{2} = 2 (a^{2} + b^{2}) o n L H S] \Rightarrow 2 {(2 x)^{2} + 3^{2}} = x (8 x + 6) - (8 x + 6) + 22 \Rightarrow 2 (4 x^{2} + 9) = 8 x^{2} + 6 x - 8 x - 6 + 22 \Rightarrow 8 x^{2} + 18 = 8 x^{2} - 2 x + 16 \Rightarrow 8 x^{2} - 8 x^{2} + 2 x = 16 - 18 \Rightarrow 2 x = - 2 \Rightarrow x = - 1 H e n c e, x = - 1 i s t h e s o l u t i o n o f t h e g i v e n e q u a t i o n$

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(2 x + 3)^{2} + (2 x - 3)^{2} = (8 x + 6) (x - 1) + 22

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(2 x + 3)^{2} + (2 x - 3)^{2} = (8 x + 6) (x - 1) + 22

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