Question

if 2(a2+b2)=(a+b)2,then show that a=b

Answer 1

Solution

2 (a²+b²) = (a+b)²

2a² + 2b² = a² + 2ab + b² ---------------------------- as (a + b)² = a² + 2ab + b²

2a² - a² + 2b² - b² – 2ab = 0

a² + b² – 2ab = 0 ------------------------- as (a – b)² = a² – 2ab + b²

(a – b)² = 0

a – b = 0

a = b

Hence proved

Answer 2

Given :

2(a²+b²)=(a+b)²

2a²+ 2b²=(a+b)²
Formula used
[ (a+b)² = a² + b² + 2ab]

2a²+2b²=  a²+ b² + 2ab

2a²- a² +2b² -b²   =  2ab

a²+ b²=  2ab

a² + b² - 2ab=0
Formula used
[ (a-b)²= a²+ b² - 2ab]

(a-b)²=0
Taking square root on both sides
a-b =0 -----------------------------------------------------------------------------------------------------
a = b
Henceproved---------------------------------------------------------------------------------------Hope this will help you....