Question

Explain why an equation of the form $\sqrt{\mathbf{x}}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0}$has no solution.

Short answer

$\sqrt{\mathbf{x}}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0}$ has no solutions.

Step-by-step solution

Step 1. Given Information:

$\sqrt{\mathbf{x}}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0}$

Step 2. Finding solution:

$$\begin{gathered} \sqrt{\mathbf{x}}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0} \\ \sqrt{\mathbf{x}}\mathbf{=}\mathbf{-}\mathbf{1} \\ \mathit{x}\mathbf{=}{\left(-1\right)}^{\mathbf{2}} \\ \mathit{x}\mathbf{=}\mathbf{1} \end{gathered}$$

Step 3. Checking the solution:

$$\begin{gathered} \mathit{x}\mathbf{=}\mathbf{1} \\ \sqrt{\mathbf{x}}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0} \\ \sqrt{\mathbf{1}}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{0} \\ \mathbf{1}\mathbf{+}\mathbf{1}\mathbf{\ne }\mathbf{0} \\ \mathit{H}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{}\mathit{i}\mathit{t}\mathbf{}\mathit{h}\mathit{a}\mathit{s}\mathbf{}\mathit{n}\mathit{o}\mathbf{}\mathit{s}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{s}\mathbf{.} \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{=}\mathbf{1}\mathbf{}\mathit{i}\mathit{s}\mathbf{}\mathit{a}\mathit{n}\mathbf{}\mathit{e}\mathit{x}\mathit{t}\mathit{r}\mathit{a}\mathit{n}\mathit{e}\mathit{o}\mathit{u}\mathit{s}\mathbf{}\mathit{s}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{.} \end{gathered}$$