SOLUTION: 1) the sum of the squares of 2 consecutive positive odd number is 103 greater than their product. Find the 2 numbers. 2) The product of 3 consecutive positive integers is 65 tim

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Question 773500: 1) the sum of the squares of 2 consecutive positive odd number is 103 greater than their product. Find the 2 numbers.
2) The product of 3 consecutive positive integers is 65 times their total sum. Find the 3 integers.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(1) The two numbers are as 2n+1 and 2n+3.

%282n%2B1%29%5E2%2B%282n%2B3%29%5E2=103%2B%282n%2B1%29%282n%2B3%29
4n%5E2%2B4n%2B1%2B4n%5E2%2B12n%2B9=103%2B4n%5E2%2B8n%2B3
8n%5E2%2B16%2B10=4n%5E2%2B8n%2B106
4n%5E2%2B8n-96=0
n%5E2%2B2n-24=0

%28n-4%29%28n%2B6%29=0
We use the POSITIVE solution to n.
n=4.

The numbers are 2%2A4%2B1=9
and
2%2A4%2B3=11
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The numbers are 9 and 11
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