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?
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
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
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