Question

Find two consecutive integers whose product is 702

Answer 1

Greetings and Happy Holidays!

Let x represent the smaller integer.

We can create an algebraic equation to solve for the numbers:

`(x)(x+1)=702`

Distribute the parenthesis:

`x^2+x=702`

Add -702 to both sides:

`(x^2+x)+(-702)=(702)+(-702)`


`x^2+x-702=0`

Factor the Complex Trinomial:

`x^2-26x+27x-702=0`


`x(x-26)+27(x-26)=0`


`(x-26)(x+27)=0`

Set Factors to Equal 0:

`x-26=0`


`x=26`

or


`x+27=0`


`x=-27`

The Answer Is:

`\boxed{x=26 x=-27}`

The two consecutive numbers can be either: 26,27 or -27,-26

I hope this helped!
-Benjamin