SOLUTION: I already know the answer to this problem, I got 8 and 16. But I was wondering if there is a different strategy to use besides quess and check to solve this. "Two numbers differ

Question 245229: I already know the answer to this problem, I got 8 and 16. But I was wondering if there is a different strategy to use besides quess and check to solve this.
"Two numbers differ by 8, and the sum of their squares is 320. Find the two numbers."
Thanks
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write equations for each phrase
;
"Two numbers differ by 8,
x - y = 8
or
x = y + 8
:
the sum of their squares is 320.
x^2 + y^2 = 320
:
Replace x with (y+8)
(y+8)^2 + y^2 = 320
:
FOIL
y^2 + 16y + 64 + y^2 = 320
:
A quadratic equation
2y^2 + 16y + 64 - 320 = 0
2y^2 + 16y - 256 = 0
:
Simplify, divide by 2
y^2 + 8y - 128 = 0
Factor
(y+16)(y-8) = 0
:
Two solutions
y = 8, then x = 16
Or
y = -16 then x = -8

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