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Question 417548: Find three consecutive even integers such taht the square of the sum of the first and second integers is equal to twice the third integer.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Find three consecutive even integers such taht the square of the sum of the first and second integers is equal to twice the third integer.
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Let x = first of three consecutive even integers
then
x+2 = second integer
x+4 = third integer
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(x + x+2)^2 =2(x+4)
(2x+2)^2 =2x+8
(2x+2)(2x+2) =2x+8
4x^2 + 8x + 4 = 2x + 8
4x^2 + 6x + 4 = 8
4x^2 + 6x - 4 = 0
2x^2 + 3x - 2 = 0
(2x-1)(x+2) = 0
x = {1/2, -2}
since we were looking for an integer we can throw out the 1/2 leaving:
x = -2
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solution: -2, 0, 2
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