Answer
The provided statement is false and the correct statement is “The solution set of ${{x}^{2}}>25$ is $\left( -\infty ,-5 \right)\cup \left( 5,\infty \right).$ ”
Work Step by Step
The provided inequality is:
${{x}^{2}}>25$
Rewrite, the provided inequality as:
${{x}^{2}}-25>0$
In order to get the solution of ${{x}^{2}}>25$ , first equate the function to $0$ , that is solve ${{x}^{2}}-25=0$.
Then,
$\begin{align}
& {{x}^{2}}-25=0 \\
& {{x}^{2}}-{{5}^{2}}=0 \\
& \left( x-5 \right)\left( x+5 \right)=0
\end{align}$
Equating each factor to 0,
$x=-5$ or $x=5$
Therefore, the solution set of ${{x}^{2}}>25$ is $\left( -\infty ,-5 \right)\cup \left( 5,\infty \right).$
And thereby, the provided statement is false.
The provided statement is false and the correct statement is “The solution set of ${{x}^{2}}>25$ is $\left( -\infty ,-5 \right)\cup \left( 5,\infty \right).$ ”
