Question

If xy = 6 and x+y = 5 then the value of x^4
+ y^4 is :

Answer 1

Answer:

xy=6 and x+y=5

$o, x⁴+y⁴

=(x²)² + (y²)²

We know that,

(x²)²+(y²)² +2x²y²=(x²+y²)²

(x²)²+(y²)²=(x²+y²)²-2x²y².........(i)

Similarly,

x²+y²+2xy = (x+y)²

x²+y²=(x+y)²-2xy

Putting values,

x²+y²=5²-12 =25-12=13...........(ii)

Comparing (i) and (ii),

x⁴+y⁴=13² - 2x²y²

= 169-2(xy)²

=169-2(6)²

=169-72

=97

Hope you got it.......