SOLUTION: Number Sense: "The sum of two numbers is eleven. The sum of the squares of the same two numbers is sixty-one. Find the two numbers"

Question 606473: Number Sense: "The sum of two numbers is eleven. The sum of the squares of the same two numbers is sixty-one. Find the two numbers"
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the numbers be x & y
x+y = 11
x^2+y^2= 61
x=11-y
x^2=(11-y)^2
substitute x
(11-y)^2+y^2= 61
121-22y+y^2+y^2=61
2y^2-22y+121=61
2y^2-22y+60=0
/2
x^2-11y+30=0
x^2-6y-5y+30=0
x(x-6)-5(x-6)=0
(x-6)(x-5)=0
x= 5 OR 6
so y= 6 OR 5
(5,6) OR (6,5)

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