The product of two consecutive even internet’s is equal to 30 more than the first. Find the intergers

Question

Show all work (let statements)

Answer 1

Two consecutive even integers:

n and n + 2

n(n + 2) = n + 30

Can you solve for n and answer?

Answer 2

Let N be the first integer. Then N+2 is the next even integer. Expressing what we know:

N * (N+2) = N + 30

N^2 + 2N = N + 30

N^2 + N = 30

therefore

N * (N+1) = 30

therefore N = -6 since -6 * (-5) = 30.

the second integer is

N + 2 = -4.

Working it by the quadratic formula:

N^2 + N - 30 = 0

N = {-1 +/- sqrt(1 + 4 * 1 * 30} / 2

N = (-1/2) +/- sqrt(121)/2 = (-1/2) +/- 11/2

therefore N = 5 or -6

N = 5 is not even so

N = -6 as before.

Checking

(-6)*(-4) = 30 + (-6) - check!