SOLUTION: The sum of two integers is 7 and the sum of their squares is 37.  Find the integers.

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Question 1150395: The sum of two integers is 7 and the sum of their squares is 37.  Find the integers.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=7%2Cx%5E2%2By%5E2=37%29

%28x%2By%29%28x%2By%29=7%2A7
x%5E2%2B2y%5E2%2B2xy=7%2A7
37%2B2xy=49
2xy=12
xy=6

y=7-x
-
x%287-x%29=6
-x%5E2%2B7x=6
-x%5E2%2B7x-6=0
x%5E2-7x%2B6=0
%28x-1%29%28x-6%29=0
-
system%28x=1%2Cor%2Cx=6%29

The integers are 1 and 6.

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Given that the sum of the two integers is 7, let the two integers be x and (7-x). Then

%28x%29%5E2%2B%287-x%29%5E2+=+37
x%5E2%2B49-14x%2Bx%5E2+=+37
2x%5E2-14x%2B12+=+0
x%5E2-7x%2B6+=+0
%28x-6%29%28x-1%29+=+0

x = 6 and 7-x = 1; or x=1 and 7-x = 6.

Either way, the two integers are 6 and 1.

Of course, if a formal algebraic solution is not required, you can find the answer in practically no time by trial and error.