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

Question 280834: 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 oberobic(2304) (Show Source): You can put this solution on YOUR website!
x + y = 7
x = 7-y
.
x^2 + y^2 = 29
.
(7-y)^2 + y^2 = 29
(7-y)(7-y) +y^2 = 29
49 -7y - 7y + y^2 + y^2 = 29
2y^2 -14y + 49 = 29
2y^2 - 14y + 49 - 29 = 0
2y^2 - 14y + 20 = 0
y^2 - 7y + 10 = 0
(y-2)(y-5) = 0
.
y=2 OR y=5
.
But it is possible that one of these is NOT an answer.
.
Checking...
.
x+y = 7
.
Substituting y = 2, then x = 5
2^2 = 4
5^2 = 25
4+25 = 29
So, y=2 and x=5 is a solution.
.
Substituting y=5, then x = 2.
That works too.
.
Answer:
The two numbers are 2 and 5.
.
Done
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