Find the relation between $a$ and $b$ : $(a + b)^{2} = a^{2}$

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Solution

Applying the identity in ${(a + b)}^{2} = a^{2}$

${(a + b)}^{2} = a^{2}$

$a^{2} + b^{2} + 2 a b = a^{2}$

$b (b + 2 a) = 0$

$b = 0$ or $b = - 2 a$

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