Finding unknown variables

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 x and y represent the first two numbers

Let a and b represent the two new numbers

xy=ab

a-b < 10

x-y = 1

x + y > 7

Am i on the right path?

What do I do next?

Re: Finding unknown variables

I think the first sentence means that you have two numbers, say x and y, and they are each squared... this gives you x^2 and y^2 (two "new numbers").

Then x^2 - y^2 < 10

x - y = 1

x + y > 7

Multiply the last two together to get

x^2 - y^2 = (x + y)(x - y) > 7 * 1 = 7

Re: Finding unknown variables

I'm still at a loss.I don't quite get it.

Anyone has further leads?

Re: Finding unknown variables

Are you aware of the difference of two squares? We have two numbers, and . We are told they are multiplied by themselves, to give and .

We are told then that the difference of the new numbers is less than , so

Using the difference of 2 squares rule,

We are told that the original difference was , so

This means that

We also know that

This means that

Assuming and are integers, this doesn't leave many options when . What are the options?

Re: Finding unknown variables

We are looking at 4 and 5 ?

Re: Finding unknown variables