Question

X-y=14 , xy=-1/2 find the (x⁴-y⁴)

Answer 1

Hi ,

x - y = 14 ----( 1 )

xy = - 1/2 -----( 2 )

do the square of equation ( 1 ) ,

( x - y )² = ( 14 )²

x² + y² - 2xy = 196

x² + y² - 2 × ( - 1/2 ) = 196

x² + y² + 1 = 196

x² + y² = 195----( 3 )

( x + y )² = x² + y² + 2xy

= 195 + 2 × ( - 1 / 2 )

= 195 - 1

= 194

x + y = ±√194----( 4 )

x⁴ - y⁴ = ( x² )² - ( y² )²

= ( x² + y² ) ( x² - y² )

= 195 × ( x + y ) ( x - y )

= 195 × ( ± √194 ) × 14

= ± 2730 × √194

I hope this helps you.

:)