Question

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

Answer 1

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 :

`color(blue)(a^2 + b^2 )= 13`
Substituting possible values for integers as: `color(blue)(a = 2 , b=3`

We obtain:
`color(blue)(2^2 + 3^2 )= 13`

`color(blue)(4 + 9 )= 13`

So in terms of ordered pairs , the integers are:
`color(blue)(a,b) =(3,2) or (2,3)`

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)`