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

1 Answer
Jul 3, 2015

Answer:

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)#