SOLUTION: One number is 3 smaller than another number. The square of the larger number is 9 larger than ten times the smaller number. Find the numbers.

Question 167026: One number is 3 smaller than another number. The square of the larger number is 9 larger than ten times the smaller number. Find the numbers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let be the larger number. That means that the smaller number is . The square of the larger number is . Ten times the smaller number is and the square of the larger number is larger than that, so:

Hence, or

Check:

If the larger number is 3, then the smaller number must be 0, 3 squared is 9 which is 9 larger than ten times zero. Checks.

If the larger number is 7, then the smaller number must be 4, 7 squared is 49 which is 9 larger than 10 times 4 (40).
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