# If the sum of the squares of three consecutive integers is 194, what are the numbers?

##### 2 Answers

#### Explanation:

There are two possible scenarios, either the three numbers go even-odd-even or they go odd-even-odd. Any even number can be written as

We now have a quadratic we can solve for k.

These are not integer values so this is not the case.

Trying the second case, we have:

Factorising our quadratic gives;

so k is 3 or -5. This means our numbers are:

Three consecutive integers are

#### Explanation:

Let the three numbers be

Or

Hence

Three consecutive integers are