SOLUTION: The sum of two numbers is 17 and the sum of their square is 145. Find the larger number.

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Question 126736: The sum of two numbers is 17 and the sum of their square is 145. Find the larger number.
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) About Me  (Show Source):
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Y-9)(Y-8)=0
X+Y=17 OR X=17-Y
X^2+Y^2=145
(17-Y)^2+Y^2=145
289-34Y+Y^2+Y^2=145
2Y^2-34Y+289-145=0
2Y^2-34Y+144=0
2(Y^2-17X+72)=0
2(Y-9)(Y-8)=0
Y-9=0
Y=9 ANSWER FOR THE LARGER NUMBER.
Y=-8=0
Y=8 ANSWER FOR THE SMALLER NUMBER.
PROOF
8^2+9^2=145
64+81=145
145=145

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If one number is x and the other y, their sum, x + y is 17. The sum of their squares, x%5E2%2By%5E2=145.

Since x%2By=17, y+=+17-x, so

x%5E2%2By%5E2=145
x%5E2%2B%2817-x%29%5E2=145
x%5E2%2B%28289-34x%2Bx%5E2%29=145
2x%5E2-34x%2B289-145=0
2x%5E2-34x%2B144=0
x%5E2-17x%2B72=0
-8%2A-9=72 and -8%2B%28-9%29=+-17

%28x-8%29%28x-9%29+=+0

So, x is either 8 or 9, and then y is either 9 or 8. Either way, the larger number is 9.

Check: 8%2B9=17 and 8%5E2%2B9%5E2=64%2B81=145