Question

10. Find three consecutive even integers such that the product of the first and the second is 92 more

than twice the third integer.

Answer 1

10, 12, 14 or -10, -8, -6

Explanation:

We can let x represent the middle integer. Then the smaller one is x-2 and the larger one is x+2. The given relation is ...

(x-2)(x) = 92 +2(x+2)

x^2 -2x = 92 +2x +4 . . . eliminate parentheses

x^2 -4x = 96 . . . . . . . . . subtract 2x

x^2 -4x +4 = 100 . . . . . . add 4 to complete the square

(x -2) = ±√100 = ±10 . . . take the square root

x = 2 ± 10 = -8 or +12 . . . . add 2

The three integers might be ...

-10, -8, -6 or 10, 12, 14