Question

$2(a^2+b^2)$ =${(a+b)}^2$
Which of the following option will satisfy the above condition?

• A. a + b = 0
• B. 2a = b
• C. a = b
• D. a = 2b

Answer 1

The correct option is C

a = b

If we expand the RHS, we see that ${(a+b)}^2$ = $a^2+b^2$ + 2ab which is equal to the LHS.
So, according to question;
$a^2+b^2+2ab$ = $2(a^2+b^2)$
$\Rightarrow$ $a^2+b^2$ + 2ab = $2a^2+2b^2$
$\Rightarrow$ $a^2+b^2-2ab=0$ [Expansion of ${(a-b)}^2$]
$\Rightarrow$ $(a-b{)}^2=0$
$\Rightarrow$ a - b = 0
$\Rightarrow$ a = b