Question

If $2(a^2 + b^2) = (a + b)^2$ then,

• A. a = b
• B. b = 2a
• C. a = 2b
• D. a = -b

Answer 1

Answer:

A. a = b

Given:

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

Formula used:

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

Calculation:

According to the question:

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

⇒ $2(a^2+b^2)=(a^2+b^2+2ab)$

⇒ $2a^2+2b^2=a^2+b^2+2ab$

⇒ $2a^2+2b^2-a^2-b^2-2ab=0$

⇒ $a^2+b^2-2ab=0$

⇒ $(a-b)^2=0$

⇒ a – b = 0

⇒ a = b

∴ The answer is a = b.