Question 638455: The difference of two numbers is 16 and the sum of their squares is 130. Using algebraic methods determine what are the numbers? Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! The difference of two numbers is 16 and the sum of their squares is 130. Using algebraic methods determine what are the numbers?
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let x=one of 2 numbers
let y=other number
..
x-y=16
x^2+y^2=130
..
x=y+16
(y+16)^2+y^2=130
y^2+32y+256+y^2=130
2y^2+32y+126=0
y^2+16y+63=0
(y+7)(y+9)=0
y=-7
x=y+16=9
or
y=-9
x=y+16=7
..
The two pairs of numbers are: (9 and-7) and (7 and-9)
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