mba9now wrote:

If x is positive, which of the following could be the correct ordering of 1/x , 2x and x^2?

1. x^2 < 2x < 1/x

2. x^2 < 1/x < 2x

3. 2x < x^2 <1/x

I got that 1 is possible but from 2 and 3 another one is also possible according to the answer. Can someone please explain

x=1/2 I is possible (every body agrees with this)

2)

x^2 < 1/x < 2x

--> x^2-1/x<0 and 1/x-2x<0

x^3-1<0 and 2x*x-1>0 (x is positive)

(x-1)*(x2+1)<0 and x*x>1/2

(because x is postiive)

--> x<1 and x> 1/sqrt(2)

So its possible for any value > 1/sqrt(2) and <1

I and II possible.

3)

2x < x^2 <1/x

x^2-2x>0 and x^2-1/x<0

x*(x-2)>0 and x3-1<0

you know that x>0 (positive)

x-2>0 and x-1<0

x>2 and x<1 not possible at all.

only I and II possible.

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