Question

If . (2a²+b²) = (a-b)², then show that a+b=0​

Answer 1

QUESTION:

• If . (2a²+b²) = (a-b)², then show that a+b=0

ANSWER:

Given,

2(a² + b²) = (a - b)²→ 2a² + 2b²

a² + 2b² - b² = - 2ab

→ a² + b² = - 2ab . .... (i)

Now,(a + b)² = a² + b² + 2ab

But from (i) ,

we know that ,

a² + b² = - 2ab→ (a + b)²

= a² + b² + 2ab

= - 2ab + 2ab= 0

Hence, (a + b)² = 0→ (a + b)² = 0² ( proved )

Answer 2

Given:

An algebraic equation  (2a² + 2b²) = (a-b)².

To Find:

The proof of a + b  = 0.

Solution:

1. The given equation is  (2a²+2b²) = (a-b)².

2. Expand the RHS using the formula of (a-b)²,

=> (2a² + 2b²) = a² + b² -2ab. ( Simplify the equation ),

=> 2a² + 2b²  - a² -b² + 2ab = 0, ( cancel the like terms ),

=> a² + 2ab +b²  = 0,

=> (a+b)²  = 0,  

=> (a+ b)= 0

∴ Hence Proved.

Therefore, the value of a + b is 0.