SOLUTION: The sum of two numbers is seven. The sum of the squares of the two numbers is twenty-nine. Find the two numbers.

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Question 314054: The sum of two numbers is seven. The sum of the squares of the two numbers is twenty-nine. Find the two numbers.

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello, Let x be one number and y the the other. We'll set up 2 equations as:
x+y=7
x^2+y^2=29
Now do substitution:
x=7-y
Plug this into the second equation:
(7-y)^2+y^2=29 Expand it out to:
49-14y+y^2+y^2=29 Subtract 29 from both sides to get:
2y^2-14y+20=0 Factor out a 2 to get:
2(y^2-7y+10)=0 Factor:
2(y-2)(y-5)=0 Solve for y to get:
y=2
y=5
So we know x can be 2 and 5
Make sense?
RJ
www.math-unlock.com