SOLUTION: The sum of the reciprocals of two numbers is 4/15 and their product is 60. what are the numbers?

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Question 374291: The sum of the reciprocals of two numbers is 4/15 and their product is 60. what are the numbers?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the numbers be x & y
...
1/x +1/y = 4/15
(x+y)/xy = 4/15
15(x+y)=4xy
15x+15y=4xy...................1
...
xy =60
x= 60/y
...
15x+15y=4xy
15*60/y +15y = 4*60
(900+15y^2)/y = 240
900+15y^2=240y
15y^2-240y+900=0
/15
y^2-16y+60=0
y^2-10y-6y+60=0
y(y-10)-6(y-10)=0
(y-10)(y-6)=0
y = 6 OR 10
the numbers are 6 & 10
...
m.ananth@hotmail.ca