Question

If 2$(a^2+b^2)$ =${(a+b)}^2$, then ______________________ .

• 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 ${2a}^2+{2b}^2$

Equating both the terms, taking all terms on the LHS, we get $a^2+b^2$ – 2ab = 0 which is nothing but the expansion of the expression ${(a-b)}^2$= 0.

${(a-b)}^2$ can be equal to 0 only if a = b.