SOLUTION: the sum of two numbers is thirteen,and the sum of their squares is 89.find the two numbers

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Question 323055: the sum of two numbers is thirteen,and the sum of their squares is 89.find the two numbers
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=13 OR X=13-Y
X^2+Y^2=89
(13-Y)^2+Y^2=89
169-26Y+Y^2+Y^2=89
2Y^2-26Y+169-89=0
2Y^2-26+80=0
2(Y^2-13Y+40)=0
2(Y-5)(Y-8)=0
Y-5=0
Y=5 ANS. X=13-5 X=8 ANS.
Y-8=0
Y=8 ANS. X=13-8 X=5 ANS.
POOF:
5^3+8^289
25+64=89
89=89