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

Jun 29, 2016

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

${\left(x\right)}^{2} + {\left(x + 1\right)}^{2} = 13$

${x}^{2} + {x}^{2} + 2 x + 1 = 13$

$2 {x}^{2} + 2 x - 12 = 0$

$2 \left({x}^{2} + x - 6\right) = 0$

$2 \left(x + 3\right) \left(x - 2\right) = 0$

$x = - 3 \mathmr{and} 2$

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

Hopefully this helps!