The product of 3 consecutive positive even integers is 84 times their sum. Find the 3 numbers.

Answer 1

product = 84 times sum

the 3 integers are x-2, x, and x+2

(x-2)x(x+2) = 84(x-2+x+x+2)

x(x^2-4) = 84(3x) = 252x

divide by x

x^2-4 = 252

x^2 =256

x = sqr256 = 16 (since the problem asked for positive integers ignore the negative square root)

the 3 consecutive even integers are 14, 16, and 18

14(16)(18) = 4032

84(14+16+18) = 84(48) = 4032