SOLUTION: if the sum of digits of two digits number is 5 and the sum of the reciprocals of the digits is 5 / 6 than the number is

Question 465158: if the sum of digits of two digits number is 5 and the sum of the reciprocals of the digits is 5 / 6 than the number is
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x+y=5.....................1
1/x + 1/y = 5/6..............2
x+y/xy=5/6
6(x+y)= 5xy
6*5/5=xy
6=xy
x=6/y
plug in (1)
6/y+y=5
multiply by y
6+y^2=5y
y^2-5y+6=0
y^2-3y-2y+6=0
y(y-3)-2(y-3)=0
(y-3)(y-2)=0
y=3 OR 2
So x = 2 OR 3
23 OR 32

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