Question 393261: When one number is 2 more than twice another and their product is 2 more than twice their sum, what is the two number solution? I used x to represent one number and 2x + 2, which equals to x(2x + 2)= 2 + 2x + 2 = 2x^2 + 2x = 2x + 4, therefore, 2x^2 + 2x-2x = -4, 2x^2 = -4 = (2x-2)(x+2). Answer: 2 and -2?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! When one number is 2 more than twice another and their product is 2 more than twice their sum, what is the two number solution?
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Let one number be "x".
The other number is "2x+2"
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Equation:
x(2x+2) = 2(x+2x+2) + 2
2x^2 + 2x = 2x+4x+4 + 2
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2x^2 + 2x = 6x+6
2x^2-4x-6 = 0
Factor:
2x^2-6x+2x-6 = 0
2x(x-3)+2(x-3) = 0
(x-3)(2x+2) = 0
Positive solution:
x = 3
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1st number: x = 3
2nd number: 2x+2 = 2*3+2 = 8
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Cheers,
Stan H.
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