Question

Find the Value of a When a^2 - b^2 = 19
If a^2 - b^2 = 19 then a = ?

Answer 1

a^2 - b^2 = 19

We know the formula for a^2 - b^2 = (a + b)(a - b)

Now since 19 is a prime number and if (a + b)(a - b) = 19, this can mean that (a + b)(a - b) = 19 x 1 which means that (a + b) = 19 and (a - b) = 1

Solving these two equations gives us a = 10 which is our answer. Just as an additional note, b will be 9.