SOLUTION: Find three consecutive positive integers such that the sum of the squares of the first and second equals the square of the third.

Question 478021: Find three consecutive positive integers such that the sum of the squares of the first and second equals the square of the third.
Found 2 solutions by stanbon, jorel1380:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find three consecutive positive integers such that the sum of the squares of the first and second equals the square of the third.
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1st: x-1
2nd: x
3rd: x+1
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Equation:
(x-1)^2 + x^2 = (x+1)^2
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x^2-2x+1 + x^2 = x^2+2x+1
x^2 -4x = 0
x(x-4) = 0
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Positive solution:
Let x = 4
1st: x-1 = 3
2nd: x = 4
3rd: x+1 = 5
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Cheers,
Stan H.
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Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
p2+(p+1)2=(p+2)2
p2+p2+2p+1=p2+4p+4
p2-2p-3=0
(p-3)(p+1)=0
p=3 or -1
Throwing out the negative answer, we get p=3, p+1=4, and p+2=5..
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