Question

show that if 2(a²+b²)=(a+b)² than a=b

Answer 1

2(a²+b²)=(a+b)²
⇒2a²+2b²=a²+b²+2ab
⇒2a²+2b²-a²-b²-2ab=0
⇒a²+b²-2ab=0
⇒(a-b)²=0
⇒a-b=0
⇒a=b
∴a=b.