SOLUTION: Please help me solve this problem: two numbers have a different of 3.the sum of their square is 89.find the number

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Question 934780: Please help me solve this problem:
two numbers have a different of 3.the sum of their square is 89.find the number
Found 2 solutions by JulietG, MathTherapy:
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
a^2 + b^2 = 89
Process of elimination is easiest.
9^2 = 81, no whole number square rt of 8
8^2 = 64. 8-3 = 5. 5^2 = 25. 64+25=89
No need to go further. The numbers are 8 and 5.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me solve this problem:
two numbers have a different of 3.the sum of their square is 89.find the number
Let the larger number be L

Then smaller = L - 3

Being that their squares sum to 89, we get: L%5E2+%2B+%28L+-+3%29%5E2+=+89

L%5E2+%2B+L%5E2+-+6L+%2B+9+=+89

L%5E2+%2B+L%5E2+-+6L+%2B+9+-+89+=+0

2L%5E2+-+6L+-+80+=+0

2%28L%5E2+-+3L+-+40%29+=+2%280%29

L%5E2+-+3L+-+40+=+0

(L - 8)(L + 5) = 0

L, or larger number = 8       OR      - 5



If larger number = 8, then smaller number = 8 - 3, or 5

If larger number = - 5, then smaller number = - 5 - 3, or - 8



Numbers: highlight_green%28highlight_green%28system%288_and_5_or%2C-+5_and_-+8%29%29%29%29

You can do the check!! 

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