SOLUTION: find two concecutive odd numbers which are such that the square of thier sum exceeds the sum of thier square by 126

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Question 256360: find two concecutive odd numbers which are such that the square of thier sum exceeds the sum of thier square by 126
Answer by Fombitz(32388) About Me  (Show Source):
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The two numbers are N and N+2.
The square of their sum is
%28N%2BN%2B2%29%5E2=%282N%2B2%29%5E2=4N%5E2%2B8N%2B4
The sum of the squares is
N%5E2%2B%28N%2B2%29%5E2=N%5E2%2BN%5E2%2B4N%2B4=2N%5E2%2B4N%2B4
4N%5E2%2B8N%2B4%3E%282N%5E2%2B4N%2B4%29%2B126
2N%5E2%2B4N%3E126
N%5E2%2B2N-63%3E0
%28N%2B9%29%28N-7%29%3E0
For the product to be positive, both factors have to be positive or both have to be negative.
Positive.
N-7%3E=0
N%3E=7+
The two consecutive odd integers are 7 and 9.
Negative.
N%2B9%3C=0
N%3C=-9
The two consecutive odd integers are -9 and -7.