If $(x + y)^{2} = (x - y)^{2}$ , mark the true statement.

x = y

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x = - y

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x = 0

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y = 0

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x = 0

and

y = 0

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Solution

The correct option is E $x = 0$ and $y = 0$
Given, ${(x + y)}^{2} = {(x - y)}^{2}$
$\Rightarrow x^{2} + y^{2} + 2 x y = x^{2} + y^{2} - 2 x y$
$\Rightarrow 2 x y = - 2 x y$
$\Rightarrow x y = 0$
$\Rightarrow x = 0$ and $y = 0$

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