SOLUTION: Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Find the three integers.

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Question 195927: Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Find the three integers.
Answer by nerdybill(7384) About Me  (Show Source):
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Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Find the three integers.
.
Let x = first consecutive even integer
then
x+2 = second consecutive even integer
x+4 = third consecutive even integer
.
(x+4)^2 = (x+2)^2 + 100
(x+4)(x+4) = (x+2)(x+2) + 100
x^2+8x+16 = x^2+4x+4 + 100
x^2+8x+16 = x^2+4x+104
8x+16 = 4x+104
4x+16 = 104
4x = 88
x = 22
.
The three integers: 22, 24, 26