SOLUTION: if x and y are positive with x minus y = 2 and xy = 24, then 1/x plus 1/y is equal to -----------?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: if x and y are positive with x minus y = 2 and xy = 24, then 1/x plus 1/y is equal to -----------?      Log On


   

Question 935201: if x and y are positive with x minus y = 2 and xy = 24, then 1/x plus 1/y is equal to -----------?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x-y=2%2Cxy=24%29.
Find 1%2Fx%2B1%2Fy?


1%2Fx%2B1%2Fy
y%2Fxy%2Bx%2Fxy
%28y%2Bx%29%2F%28xy%29
OR
%28x%2By%29%2F%28xy%29
%28x%2By%29%2F24 using one of your given equations.


First equation of the system gives x=y+2.
Substitution gives %28y%2B2%29y=24
y%5E2%2B2y=24
y%5E2%2B2y-24=0
%28y-4%29%28y%2B6%29=0, and according to the restriction given for x and y, must choose highlight_green%28y=-6%29. This makes highlight_green%28x=-4%29.

FINISH THE ANSWER:
%28-4-6%29%2F24
-10%2F24
highlight%28-5%2F12%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

if x and y are positive with x minus y = 2 and xy = 24, then 1/x plus 1/y is equal to -----------?


1%2Fx+%2B+1%2Fy = 1%2F6+%2B+1%2F4, or highlight_green%285%2F12%29