SOLUTION: A number minus twice its reciprocal is the same as the reciprocal of four times the number. find the number. I have the equation as x-2 1/x = 1/4x then i multiplied 2 by 1/x a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A number minus twice its reciprocal is the same as the reciprocal of four times the number. find the number. I have the equation as x-2 1/x = 1/4x then i multiplied 2 by 1/x a      Log On


   

Question 297418: A number minus twice its reciprocal is the same as the reciprocal of four times the number. find the number.
I have the equation as x-2 1/x = 1/4x
then i multiplied 2 by 1/x and got 2/x
Then i changed the x/1-2/x into the same base so we can subtract and got (x^2-2)/x + 1/4x
From there i am lost.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n= the number
n+-+2%2A%281%2Fn%29+=+1%2F%284n%29
Multiply both sides by n
n%5E2+-+2+=+1%2F4
Multiply both sides by 4
4n%5E2+-+8+=+1
4n%5E2+=+9
n%5E2+=+9%2F4
Take the square root of both sides
n+=+3%2F2
and
n+=+-3%2F2
check answer:
n+-+2%2A%281%2Fn%29+=+1%2F%284n%29
%28-3%2F2%29+-+2%2A%281%2F%28-3%2F2%29%29+=+1%2F%284%2A%28-3%2F2%29%29
Multiply both sides by 2
-3+-+4%2A%28-2%2F3%29+=+-1%2F3
-3+%2B+8%2F3+=+-1%2F3
-9%2F3+%2B+8%2F3+=+-1%2F3
-1%2F3+=+-1%2F3
OK