Find three consecutive even integers such that the product of the first and the second is one half the product of the second and third.

Answer 1

Hello.

So, since the integers are even and consecutive, we can call them:

x, x + 2, x + 4

If the product of the first and the second is 1/2 the product of the 2nd and 3rd then:

(x)(x + 2) = (1/2)(x + 2)(x + 4)

x² + 2x = (1/2)(x² + 6x + 8)

Let's multiply both sides by 2 to get rid of the fraction:

2x² + 4x = x² + 6x + 8

x² - 2x - 8 = 0

(x - 4)(x +2) = 0

The solutions to this equation are 4, -2

Therefore the solutions are:

(4, 6, 8)

and

(-2, 0, 2)