Question

IF 2(a²+b²)=(a+b)²,then show that a=b ?​

Answer 1

Answer:

IF 2(a²+b²)=(a+b)²

2a²+2b²=a²+b²+2ab

a²+b²=2ab

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the two identities that :

1.

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

2.

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

GIVEN

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

TO SHOW

$a = b$

EVALUATION

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

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

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

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

$\implies \: {(a - b)} = 0$

$\implies \: a = b$

Hence proved