Question

x-y=2 & xy=2 find x^2-y^2

Answer 1

Heya!!

x² - y² = ?

=>

x² - y² = ( x + y ) × ( x - y )

=>

x² - y² = 2 × ( x + y )

_______________________________

x - y = 2 And xy = 2 Given

SQUARING BOTH SIDES

( x - y )² = 2²

=>

x² + y² - 2xy = 4

=>

x² + y² = 8

=>

( x + y )² -2xy = 8

Becoz x² + y² = ( x + y )² -2xy

=>

( x + y ) = √12 OR ( x + y ) = -√12

( x + y ) = 2√3 OR ( x + y ) = -2√3

=>

So, x² - y² = 2 ( 2√3 ) = 4√3

OR

x² - y² = -2 ( 2√3 ) = -4√3