Question

if x+1/x=4,then x-1/x ia equal to

Answer 1

Since x+1/x=4
x+1=4x
x-4x=-1
-3x=-1
x=1/3
Therefore the value of x -1/x is equal to 1/3-1/1/3
1-3/3/1/3
-2/3/1/3
-2
It is the answer..

Answer 2

Here
x+1/x =4. (1)
let x-1/x=k. (2)
squaring equation (1) we get
x²+1/x²+2x.1/x=16
or,x²+1/x²+2=16
or,x²+1/x²=14. (3)

Now
squaring equation (2) we get
x²+1/x²-2x.1/x=k²
or,x²+1/x²-2=k²
or,x²+1/x²=k²+2 (4)
comparing equation (3) and(4) we get
k²+2=14
or,k²=12
or,k=√12
or,k=±2√3
which is the required answer.