If $(x + 1)^{2} - (x - 1)^{2} = 32$ , find the value of $x$ .

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Solution

The correct option is C $8$
We know $(x + 1)^{2} = x^{2} + 2 x + 1$
and $(x - 1)^{2} = x^{2} - 2 x + 1$
As given ,
$(x + 1)^{2} - (x - 1)^{2} = 32$
$x^{2} + 2 x + 1 - (x^{2} - 2 x + 1) = 32$
$x^{2} + 2 x + 1 - x^{2} + 2 x - 1 = 32$
$4 x = 32$
$x = 8$
Hence, option C is correct.

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