Find the intergers?

Question

1) The product of two consecutive positive integers is 109 more than their sum. Find the integers.

2) The product of two consecutive positive odd integers is 1 less thank four times their sum. Find the integers.

3) The product of two consecutive even integers is 24 more than three times the larger integer. Find the integers.

Can you please show me how to work these questions out?

Thank you!!!!

Answer 1

I will do one for you, so that you can see how they are done. Then you can do your own homework and do the rest.

1) Two consecutive positive integers can be represented as X and X+1.
We also know that X(X+1) = X + (X+1) + 109 or
X^2 + X = 2X + 110, or
X^2 - X - 110 = 0, or
(X - 11)(X + 10) = 0

So the answer is (11, 12) - since we are only looking at positive integers. If we include the negative ones, the answer would be (-9, -10) since the difference between -19 and 90 is 109 as well.

Checking:
11* 12 = 132
11 + 12 = 23
132 - 23 = 109 and we are correct.

Good luck!
[I have shown you how to work these answers out, just as you asked. Please don't reward someone who just feeds you the answers without showing you the work. Thanks!]

Answer 2

1) a * (a+1) = a + (a + 1) + 109

a^2 + a = 2a +110

a^2 - a - 110 = 0

use quadratic formula to solve for a

(1 +/- sqrt (1+440))/2

pick positive answer, which is 11

The integers are 11, 12

For the rest of the problems, do your own homework!