If $2 (a^{2} + b^{2}) = (a + b)^{2}$ , then show that $a = b$ .

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Solution

Acccording to question,
$2 (a^{2} + b^{2}) = (a + b)^{2}$
$\Rightarrow 2 a^{2} + 2 b^{2} = a^{2} + b^{2} + 2 a b$
$\Rightarrow a^{2} + b^{2} - 2 a b = 0$
$\Rightarrow (a - b)^{2} = 0$
Therefore,
$\Rightarrow a = b$

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