SOLUTION: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers

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Question 122437: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers
Answer by solver91311(24713) About Me  (Show Source):
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If the first even integer is n, the second is n + 2, and the third is n + 4.


We are given that %28n%2B4%29%5E2=%28n%2B2%29%5E2%2B76


Expand the binomials, collect terms, and solve for n


%28n%2B4%29%5E2=%28n%2B2%29%5E2%2B76
n%5E2%2B8n%2B16=n%5E2%2B4n%2B4%2B76
8n-4n=4%2B76-16
4n=64
n=16


So the first even integer is 16, the second is 18, and the third is 20.




Check the answer

20%5E2=400


18%5E2=324 and 324%2B76=400