Question

if 2(a²+b²)=(a+b)²then show that a=b
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Answer 1

Step-by-step explanation:

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

$2( {a}^{2} + {b}^{2} ) = {a}^{2} + {b}^{2} \: + 2ab$

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

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

${a}^{2} + {b}^{2} - 2ab = 0$

${(a - b)}^{2} = 0$

Taking Square root on both sides

$a - b = 0$

$a = b$