word problem

[sandra91767]

Hello everyone: A co-woker asked me to help her with this word problem; frankly, I have not been able to figure it out. I am a returning student after 20 years and need all the help I can get. I'm sure I will be using this valuable resource frequently. Thank you all for any help provided. The word problem is the following:

Find two consecutive positive numbers such that the product of the sum and difference of the numbers plus eight is the sum of their squares.

 

[Loren]

Start by naming things. If you call one positive integer x, then the next positive consecutive integer will be called x+1.

The product of the sum and difference of the numbers plus eight is the sum of their squares.

The sum of the numbers would be x + x+1.
The difference of the numbers would either x-(x+1) or x+1-x.
One square would be x[sup:29dery4f]2[/sup:29dery4f].
The other square would be (x+1)[sup:29dery4f]2[/sup:29dery4f]

Now, put that information into the sentence above and solve for x.

 

[mmm4444bot]

You're the student, but your coworker has this word problem? :?

n = the first number

n + 1 = the next number

The "sum" means: n + 1 + n

The "difference" means: n + 1 - n

So their sum is 2n + 1, and their difference is 1. (I'm assuming they mean the positive difference, which is obviously 1 between two consecutives.)

The "product" means the sum times the difference.

(2n + 1)*(1) = 2n + 1

"Plus eight" means add eight to this product.

2n + 1 + 8

That's 2n + 9

We're told that this amount equals the sum of the squares of each number.

n^2 + (n + 1)^2 = 2n + 9

This is a quadratic equation. Do you know howto solve it?