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?**

Re: Find the Unknown Variable

note ...

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

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?

Re: Find the Unknown Variable

You know, as skeeter noted that:

$\displaystyle (a-b)(a+b)<10$

$\displaystyle (a+b)>7$

$\displaystyle (a-b)=1$

so: $\displaystyle 7<a+b<10$

can you continue from this?