# The product of two consecutive integers is 482 more than the next integer. What is the largest of the three integers?

##### 1 Answer
Feb 15, 2017

The largest is 24 or -20.
Both solutions are valid.

#### Explanation:

Let the three numbers be $x , x + 1 \mathmr{and} x + 2$

The product of the first two differs from the third by 482.

$x \times \left(x + 1\right) - \left(x + 2\right) = 482$

${x}^{2} + x - x - 2 = 482$

${x}^{2} = 484$

$x = \pm \sqrt{484}$

$x = \pm 22$

Check: $22 \times 23 - 24 = 482$

$- 22 \times - 21 - \left(- 20\right) = 482$

Both solutions are valid.