Competition Math Question

Question

+1

649

1

+94

Find all real numbers x and y such that

$x^2y^2+x^2+y^2+2xy=40$ and $xy + x+y=8$

Please explain your answer!

RandomUser Dec 22, 2020

Melody · Answer 1 · 2020-12-22T09:57:04

Hint:

$x^2+y^2+2xy=(x+y)^2\\ and\\ x+y=8-xy$

After I continued on a little further I found it easier to substitute z=xy and solve for z

then I solved for x and y after that.