SOLUTION: the sum of the ages of two sisters is 21. the sum of the squares of their ages is 233. what are the two ages? Their ages can be represented by x and y. x+y=21 x^2+y^2=233

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the sum of the ages of two sisters is 21. the sum of the squares of their ages is 233. what are the two ages? Their ages can be represented by x and y. x+y=21 x^2+y^2=233      Log On


   

Question 304078: the sum of the ages of two sisters is 21.
the sum of the squares of their ages is 233.
what are the two ages?
Their ages can be represented by x and y.
x+y=21
x^2+y^2=233
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=21
x^2+y^2=233
x^2+y^2+2xy = 233+2xy
(x+y)^2 = 233+2xy
21^2= 233 +2xy
441-233= 2xy
208=2xy
104 = xy
y= 104/x
x+104/x=21
x^2+104 / x = 21
x^2+104=21x
x^2-21x+104=0
x^2-8x-13x+104=0
x(x-8)-13(x-8)=0
(x-8)(x-13)=0
x=8 Or x=13
the ages are 8 and 13