Chapter 3.5, Problem 40AYU

To determine

To show:

The inequality equation ${\left(x-2\right)}^2>0$ has one real number but it is not the solution for inequality equation.

Explanation of Solution

Given Information:

  ${\left(x-2\right)}^2>0$

Proof:

The given equation is:

  $\begin{array}{l}{\left(x-2\right)}^2>0\\ \left(x-2\right)\left(x-2\right)>0\\ x=2\end{array}$

So, the given equation contains exactly one real number but it is not its solution because the given inequality equation is true for all possible values or calculated value of $\left(x\right)$ .

When the estimated values are true for inequality equations then the values are only considered as real numbers not the solution for inequality equation.

It means that when inequality equation contains real number but that is not its solution, the equation has no solution.

Hence, proved.