Posted by **Anonymous** on Wednesday, April 13, 2011 at 12:54am.

Suppose x and y are real numbers such that xy = 9 and x2y + xy2 + x + y = 100. What is the integer value of x2 + y2? (Target Round #6)

- 8th grade math -
**Jai**, Wednesday, April 13, 2011 at 1:19am
observe that we can factor xy from (x^2)y + x(y^2):

(x^2)y + x(y^2) + x + y = 100:

xy [ x + y ] + x + y = 100

then we can factor (x + y):

(x + y)(xy + 1) = 100

since xy = 9,

(x + y)(9 + 1) = 100

(x + y)(10) = 100

x + y = 10

getting its square,

(x + y)^2 = 100

x^2 + 2xy + y^2 = 100

since xy = 9,

x^2 + y^2 + 2*9 = 100

x^2 + y^2 + 18 = 100

x^2 + y^2 = 82

hope this helps~ :)

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