Question

If x+y=8,xy=15,find x4+x2y2+y4

Answer 1

Answer:

931

Step-by-step explanation:

x + y = 8

x = 8-y

xy = 15

(8-y) y = 15

8y - y^2 = 15

y^2 - 8y + 15 = 0

y^2 - 3y - 5y + 15 = 0

y ( y - 3 ) - 5 ( y - 3 ) = 0

( y - 3 ) ( y - 5 ) = 0

y = 5 or y = 3

x = 3 or x = 5

x^4 + y^4 + ( xy )^2 = 3^4 + 5^4 + 15^2

= 81 + 625 + 225 = 931