Question

Guys pleas answer.
Example 6. On what basis can we say that we should take (x+y)²??? ​

Answer 1

We know the value of x+y and also of xy. We have to find x^2+y^2. If you think, squarring both sides will give you (x+y)^2 which will be x^2+y^2+2xy. You can use this to find x^2+y^2. It's a bit of intuition.

Answer 2

It's just a way by using an identity.... Such questions are designed to be solved by using identities...

Given:

x+y = 12

xy = 32

(x+y)² = x² + y² + 2xy

=> (12)² = x² + y² + 2(32)

=> 144 = x² + y² + 64

=> 144 - 64 = x² + y²

=> x² + y² = 80.