Chapter 6, Problem 9CR

To determine

To Solve:

  $3-2\sqrt{x}=7$

Answer to Problem 9CR

(d)

Explanation of Solution

Given :

The equation is :

  $3-2\sqrt{x}=7$

  $\begin{array}{l}a.\left\{-2\right\}\\ b.\left\{4\right\}\\ c.\left\{-4\right\}\\ d.\varphi \end{array}$

Calculation:

Given:

  $\begin{array}{l}3-2\sqrt{x}=7\\ \Rightarrow 3-2\sqrt{x}+2\sqrt{x}=7+2\sqrt{x}\mathrm{......}[\text{add }2\sqrt{x}\text{ each side]}\\ \Rightarrow 3-7=7+2\sqrt{x}-\mathrm{7................}[\text{subtract 7 from each side]}\\ \Rightarrow -4=2\sqrt{x}\\ \Rightarrow \frac{2\sqrt{x}}{2}=\frac{-4}{2}\mathrm{............................}[\text{divide each side by 2]}\\ \Rightarrow \sqrt{x}=-2\\ \text{Since square root is always non-negative }\text{.}\\ \text{So, }\sqrt{x}\ge 0.\\ Hence,\sqrt{x}=-2<0\text{ is impossible }\text{.}\\ \text{So, the solution set for the given equation is empty}\text{.}\end{array}$

So, (d) is the correct option.