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)   (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)   (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 - 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: 

You can do the check!! 

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