SOLUTION: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

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Question 48776: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
Answer by venugopalramana(3286) About Me  (Show Source):
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Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
let the 3 CONSECUTIVE EVEN integers be 2n,2n+2,2n+4
SQUARE OF THIRD = (2N+4)^2
SQUARE OF SECOND=(2N+2)^2
DIFFERENCE =(2N+4)^2-(2N+2)^2=76=4(N+2)^2-4(N+1)^2
(N+2)^2-(N+1)^2=19
(N+2+N+1)(N+2-N-1)=19
2N+3=19
2N=16
N=8
HENCE THE NUMBERS ARE
2*8=16,18,20