SOLUTION: two numbers different by 9,and the sum of their reciprocals is 5/12.find the numbers?

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Question 518930: two numbers different by 9,and the sum of their reciprocals is 5/12.find the numbers?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x-y =9
x=y+9
1/x+1/y =5/12
substitute x
1%2Fy%2B%281%2F%28y%2B9%29%29=5%2F12
muktiply by y(y+9) the LCD
%28%28y%2B9%29%2By%29%2F%28y%28y%2B9%29%29=5%2F12
%282y%2B9%29%2F%28y%28y%2B9%29%29=5%2F12
cross multiply
12(2y+9)=5(y(y+9))
24y+108=5y^2+45y
5y^2+21y-108=0
Find the roots of the equation by quadratic formula

a= 5 , b= 21 , c= -108

b^2-4ac= 441 + 2160
b^2-4ac= 2601 %09sqrt%28%092601%09%29=%0951%09
y=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
y1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
y1=( -21 + 51 )/ 10
y1= 3
y2=( -21 -51 ) / 10
y2= -7.2
12 & 3 is one of the solution.
-7.2 & 1.8
m.ananth@hotmail.ca