Answer
$f = 1.59\times 10^5~Hz$
$X_L = X_C = 1.0~\Omega$
Work Step by Step
We can equate the reactances to find the required frequency:
$X_L = X_C$
$\omega ~L = \frac{1}{\omega~C}$
$\omega^2 = \frac{1}{L~C}$
$(2\pi~f)^2 = \frac{1}{L~C}$
$f^2 = \frac{1}{4~\pi^2~L~C}$
$f = \frac{1}{2\pi~\sqrt{L~C}}$
$f = \frac{1}{(2\pi)~\sqrt{(1.0\times 10^{=6}~H)(1.0\times 10^{-6}~F)}}$
$f = 1.59\times 10^5~Hz$
We can find the value of the reactance:
$X_L = \omega ~L$
$X_L = 2\pi~f ~L$
$X_L = (2\pi)~(1.59\times 10^5~Hz) ~(1.0\times 10^{-6}~H)$
$X_L = 1.0~\Omega$
Therefore, $X_L = X_C = 1.0~\Omega$
