Question

if
$2( {a}^{2} + {b}^{2} ) = ( {a + b)}^{2}$
then prove that a=b​

Answer 1

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

(Using the identity $(a + b)^{2}$ = $a^{2}$ + 2ab + $b^{2}$)

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

(Bringing everything to the left side)

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

(Using the identity $(a - b)^{2}$ = $a^{2}$ - 2ab + $b^{2}$)

Hence,

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

a - b = 0

a = b

Q.E.D.