Question

The sum of the squares of two consecutive positive integers is 13. How do you find the integers?

Answer 1

Let the numbers be `x` and `x + 1`.

`(x)^2 + (x + 1)^2 = 13`

`x^2 + x^2 + 2x + 1 = 13`

`2x^2 + 2x - 12 = 0`

`2(x^2 + x - 6) = 0`

`2(x + 3)(x - 2) = 0`

`x = -3 and 2`

Hence, the numbers are `2` and `3`. Checking in the original equation yields proper results; the solution work.

Hopefully this helps!