Chapter 4.7, Problem 59STP

To determine

For what the value of x, which satisfy $\frac{1}{\sqrt{x}}<\sqrt{x}<x$ .

Answer to Problem 59STP

The value of x =2.

Explanation of Solution

Given information:

  $\begin{array}{l}\text{A}=-2\text{ C}=\frac{1}{2}\\ \text{B}=\frac{1}{4}\text{ D}=2\end{array}$

Calculation : The equation should be satisfies as,

  $\begin{array}{l}\frac{1}{\sqrt{x}}<\sqrt{x}<x\\ \frac{1}{\sqrt{2}}<\sqrt{2}<2\left(\text{Replace x with 2}\right)\\ \frac{1}{1.41}<1.41<2\\ 0.707<1.41<2\end{array}$

Hence, the value of x=2, which satisfied the equation $\frac{1}{\sqrt{x}}<\sqrt{x}<x$ .