Question

The product of two consecutive numbers is 72. Use a quadratic equation to find the two sets of numbers.

Answer 1

Given:

The product of two consecutive numbers is 72.

To find:

The two numbers by using the quadratic equation.

Solution:

Let the two consecutive numbers are x and (x+1).

The product of two consecutive numbers is 72.

`x(x+1)=72`

`x^2+x-72=0`

Splitting the middle term, we get

`x^2+9x-8x-72=0`

`x(x+9)-8(x+9)=0`

`(x+9)(x-8)=0`

Using zero product property, we get

`x+9=0` and
`x-8=0`

`x=-9` and
`x=8`

If
`x=-9`, then

`x+1=-9+1`

`x+1=-8`

If
`x=8`, then

`x+1=8+1`

`x+1=9`

Therefore, the two consecutive numbers are either 8,9 or -9,-8.