Question 410788: Find three consecutive odd interrgers such that the product of the first and the second exceeds the third by eight.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find three consecutive odd integers such that the product of the first and the second exceeds the third by eight.
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1st: 2x-1
2nd: 2x+1
3rd: 2x+3
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Equation:
(2x-1)(2x+1)-(2x+3) = 8
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4x^2-1 -2x-3 = 8
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4x^2-2x-12 = 0
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2x^2-x-6 = 0
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2x^2-4x+3x-6 = 0
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2x(x-2) + 3(x-2) = 0
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(x-2)(2x+3) = 0
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x = 2 or x = -3/2
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If x = 2:
1st: 2x-1 = 3
2nd: 5
3rd: 7
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If x = -3/2
1st: 2x-1 = -4
2nd: -2
3rd: 0
Note: These are all EVEn numbers.
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So the only answer is 3,5,7
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Cheers,
Stan H.
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