# Thread: find integers

1. ## find integers

Currently I'm learning polynomials, trinomials, and basic factoring. I don't understand this question at all.

'a' and 'b' are integers. Find the value of a and b, if a^2 - b^2 = 2 1.

2. Originally Posted by DFKnight
Currently I'm learning polynomials, trinomials, and basic factoring. I don't understand this question at all.

'a' and 'b' are integers. Find the value of a and b, if a^2 - b^2 = 2 1.
first we think of the factors of 21 that are integers. ok, we can have 21 = 1*21 or 21 = 7*3. now, file that away, we'll come back to it.

Now $a^2 - b^2 = (a + b)(a - b)$ ........the difference of two squares

$\Rightarrow (a + b)(a - b) = 21$

now we want $(a + b)$ and $(a - b)$ to be integer factors of 21.

Let's say they are 7 and 3.

set $a + b = 7$
and $a - b = 3$

$\Rightarrow \boxed{a = 5} \mbox { and } \boxed{ b = 2}$

this is one solution, there are others.

we get a new solution set if a + b = 3 and a - b = 7

and also, if we take the factors to be 1 and 21

we need more conditions if we want a unique solution