# The sum of their square is 13, what are the two integers?

Jul 3, 2015

all possible solutions for (a,b) will include :
color(blue)((a,b) =(3,2) , (3,-2) , (-3,2) , (-3,-2)),color(green)( (2,3) , (2,-3) , (-2, 3) and (-2,-3)

#### Explanation:

let the two integers be color(blue)(a and b

As per the condition :

$\textcolor{b l u e}{{a}^{2} + {b}^{2}} = 13$
Substituting possible values for integers as: color(blue)(a = 2 , b=3

We obtain:
$\textcolor{b l u e}{{2}^{2} + {3}^{2}} = 13$

$\textcolor{b l u e}{4 + 9} = 13$

So in terms of ordered pairs , the integers are:
$\textcolor{b l u e}{a , b} = \left(3 , 2\right) \mathmr{and} \left(2 , 3\right)$

Note: we can also have negative values for $a$ and $b$ as the integer is ultimately squared.

So all possible solutions for $a , b$ will include :
color(blue)((a,b) =(3,2) , (3,-2) , (-3,2) , (-3,-2)),color(green)( (2,3) , (2,-3) , (-2, 3) and (-2,-3)