Question

Find the value of (x^4+y^4 ) and (x^2-y^2)^2, when x^2 + y^2 = 5 and xy= 2.

Solve using suitable Identities..
With full stepss..​

Answer 1

On squaring, we get :-

= ( x² + y² )² + = (5)²

= (x²)² + (y²)² + 2 × x² × y² = 25

= x4 + x4 + 2(x × y)² = 25

= x4 + x4 + 2(2)² = 25

= x4 + x4 + 2 × 4 = 25

= x4 + x4 + 8 = 25

= x4 + x4 = 25 - 8

= x4 + x4 = 17

So, therefore x^4 + y^4 is 17

( Identity used :- (a - b)² = a² + b² - 2ab )

= (x² - y²)² = (x²)² + (y²)² - 2xy

= (x² - y²)² = x4 + y4 - 2xy

= (x² - y²)² = 17 - 4

= (x² - y²)² = 13