Question

If 2(a²+b²)=(a+b)²/then show tjat a=b

Answer 1

Step-by-step explanation:

2a^2+b^2=a^2+b^2+2ab

a^2+b^2-2ab=0

(a-b)^2=0

(a-b)(a-b)=0

a-b=0

a=b

Answer 2

Given, 2(a²+b²) = (a+b)²

          ⇒ 2a²+2b²-(a+b)²=0

          ⇒ 2a²+2b²-(a²+b²+2ab)=0

          ⇒ 2a²+2b²-a²-b²-2ab=0

          ⇒ a²+b²-2ab=0

          ⇒ (a-b)²=0

          ⇒ a-b=0

          ∴  a=b

Hence, it is proved.