SOLUTION: Find three consecutive integers so that the square of the second increased by the product of the other two is 199.

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Question 674805: Find three consecutive integers so that the square of the second increased by the product of the other two is 199.
Answer by stanbon(75887) About Me  (Show Source):
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Find three consecutive integers so that the square of the second increased by the product of the other two is 199.
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1st: x-1
2nd: x
3rd: x+1
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Equations:
x^2 + (x^2-1) = 199
2x^2 -200 = 0
2(x^2-100) = 0
x^2-100 = 0
(x-10)(x+10) = 0
x = 10 or x = -10
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If x = 10,
1st: x-1 = 9
2nd: x = 10
3rd: x+1 = 11
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If x = -10,
1st: x-1 = -11
2nd: x = -10
3rd: x+1 = -9
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Cheers,
Stan H.
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