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.

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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) About Me  (Show Source):
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Let x be the larger number. That means that the smaller number is x-3. The square of the larger number is x%5E2. Ten times the smaller number is 10%28x-3%29=10x-30 and the square of the larger number is 9 larger than that, so:

x%5E2=10x-30%2B9

x%5E2-10x%2B21=0

%28x-3%29%28x-7%29=0

Hence, x=3 or x=7

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).