Question

show that If 2(a²+b²)=(a+b)²then a=b

Answer 1

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

Answer 2

Given,

2(a²+b²) = (a+b)²

2a²+2b² = a²+b²+2ab

2a²-a²+2b²-b²-2ab = 0

a²+ b² - 2ab = 0

( a - b) ² = 0

a - b = 0

a = b.

Hence proved!