# Thread: Find the Unknown Variable

1. ## Find the Unknown Variable

Two numbers are each multiplied by themselves to give two new numbers. The difference between these two new numbers is less than ten; the difference between the two original numbers was one.
The two original numbers added together was more than 7. What is one of the original numbers?

Let the original numbers be a and b

And so new numbers are a^2 and b^2-Two numbers are each multiplied by themselves to give two new numbers.

a^2 - b^2 < 10- The difference between these two new numbers is less than ten.

a-b = 1 -The difference between the two original numbers was one.

a + b > 7 -The two original numbers added together was more than 7.

What do I need to do further to unravel this?

2. ## Re: Find the Unknown Variable

note ...

$a^2 - b^2 = (a-b)(a+b)$

3. ## Re: Find the Unknown Variable

Thnx But am still confused as to how I can go any further to unravel this question to find the answer to the question:

What is one of the original numbers?

4. ## Re: Find the Unknown Variable

You know, as skeeter noted that:
$(a-b)(a+b)<10$
$(a+b)>7$
$(a-b)=1$
so: $7
can you continue from this?