Answer
(a) yes
(b) no
Work Step by Step
(a) Using $x=4$, we get:
Left side:
$\displaystyle \frac{4^{3/2}}{4-6}=\frac{2^{3}}{-2}=\frac{8}{-2}=-4$
Right side:
$(4)-8=-4$
The sides match, so $x=4$ is a solution.
(b) Using $x=8$, we get:
Left side:
$\displaystyle \frac{8^{3/2}}{8-6}=\frac{(2^{3})^{3/2}}{2}=\frac{2^{9/2}}{2}=2^{7/2}$
Right side:
$(8)-8=0$
The sides do not match, so $x=8$ is not a solution.
