# 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

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 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=233Answer by mananth(12270)   (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