Question

if 2(a²+b²)=(a+b)² then show that a=b

Answer 1

2(a^2 + b^2 ) = (a + b)^2
2a^2 + 2b^2 = a^2 + b^2+ 2ab
a^2 + b^2 = 2ab
a^2 - 2ab + b^2 = 0
(a-b)^2 = 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.