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How to solve this inequality problm in the easiest way

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Source: — Problem Solving |
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by Atekihcan » Thu May 09, 2013 2:29 am
Note that the problem involves √x.
So, we can safely conclude that x > 0.

--> 1/x > 8√x
--> x√x < 1/8
--> x^(3/2) < 1/8
--> x < (1/8)^(2/3)
--> x < (1/64)^(1/3)
--> x < 1/4

So, 0 < x < 1/4
--> 0 < √x < 1/2
So, 1/√x > 2

Answer : D
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