Answer
False. The given expression becomes \[\frac{4\pm \sqrt{3}}{2}=2\pm \frac{\sqrt{3}}{2}\].
Work Step by Step
Considering
\[\frac{4\pm \sqrt{3}}{2}\]
Simplifying further
\[\begin{align}
& \frac{4\pm \sqrt{3}}{2}=\frac{4}{2}\pm \frac{\sqrt{3}}{2} \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=2\pm \frac{\sqrt{3}}{2} \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ne 2\pm \sqrt{3} \\
\end{align}\]
Therefore, the given statement is false.
The correct statement regarding the given expression is
\[\frac{4\pm \sqrt{3}}{2}=2\pm \frac{\sqrt{3}}{2}\]
