SOLUTION: There are three consecutive positive integers such that the sum of square of first and the other two is 154. The the largest number is?

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Question 1025739: There are three consecutive positive integers such that the sum of square of first and the other two is 154. The the largest number is?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry, there aren't any 3 such consecutive positive integers.
Here is why there cannot be:

5²+6²+7² = 25+36+49 = 110
6²+7²+8² = 36+49+64 = 149
7²+8²+9² = 49+64+81 = 194
8²+9²+10² = 64+81+100 = 245

See?  The sums of squares skip
right over 154.  There is no solution.

Edwin