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.

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) (Show Source): You can put this solution on YOUR website!
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
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