# How do you find two consecutive positive odd integers whose product is 143?

##### 3 Answers

#### Explanation:

Notice that consecutive odd integers will differ by

So:

#143 = (n-1)(n+1) = n^2-1#

Add

#n^2 = 144 = 12^2#

So

Since we are told that the integers are positive, use

Alternatively, just find factors of

11 and 13

#### Explanation:

Proceed as below.

Let

Rest of the steps are same as followed by others.

It is by convention, as

Expanding on AO8's answer: This approach guarantees that any number we look at is odd:

#### Explanation:

We need to be able to guarantee that we are dealing with odd numbers.

Let

Suppose n is even. Then

Suppose n is odd. Then

But in both cases

Let the first odd number be

Then the second odd number will be

We are given that the product is 143 so write the equation as:

This is saying exactly the same thing as the others but in a slightly different way! So we now have:

Divide by 4

So for my conditions

Thus the first number is:

So the second number is