Integers Math Problem (I need help please!)

Question

Find three consecutive positive even integers such that the product of the two smaller integers is 16 more than the largest. 12

Answer 1

Numbers are x, x + 2, x + 4. So x(x + 2) = (x + 4) + 16; x² + x - 20 = 0; (x + 5)(x - 4) = 0. So x = 4 or x = -5.

Because we looking for positive numbers we get 4, 6, 8

Answer 2

In this case, we first read the problem CAREFULLY, and determine we have three positive consecutive integers. Then we set up the variables as follows:

x = first integer, x + 2 = next cons. integer, and x + 4 = final positive cons. integer.

Now, we are given the information that the product of the first two numbers IS (equals) 16 plus the last integer. So the equation looks like this: x(x +2) = 16 + (x + 4) **Now we solve this equation. **

x² + 2x = 16 + x + 4 (Subtract x from both sides)

x^2 + x = 20 (Now subtract 20 from both sides)

x^2 + x - 20 = 0 (now factor the polynomial)

(x + 5)(x - 4) = 0

so our solutions are x = -5 and x = 4. Since we cannot have a negative integer, we use x = 4. The consecutive positive integers then, are 4, 6, and 8. These problems are very fun when we know what to do!