SOLUTION: Find three consecutive integers such that the product of the first two plus the product of the first and the third is 14.

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Question 659755: Find three consecutive integers such that the product of the first two plus the product of the first and the third is 14.
Answer by ReadingBoosters(3246) About Me  (Show Source):
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x; (x+1); (x+2)
(x)(x+1) + (x)(x+2) = 14
Distribute the x
x^2 + x + x^2 + 2x = 14
Combine like terms
2x^2 + 3x = 14
Set equal to 0
2x^2 + 3x - 14 = 0
( + )( - ) signs determined by -14
common multiples of 14: 1,14; 2,7
(2x + 7)(x - 2)
check by FOIL: 2x^2 - 4x + 7x - 14, which is 2x^2 + 3x -14
2x+7=0, x = -7/2: won't work
x-2=0, x = 2: correct
x+1=3, x+2=4
Proof:
(2)(3)= 6
(2)(4) = 8
6+8=14
Answer: 2, 3, 4