In an LC oscillator, if values of inductance and capacitance become...

Resonance frequency of an LC oscillations circuit is stated as

${\omega}_{0} = \dfrac{1}{\sqrt{LC}}$, here, $LandC$ represents inductance and capacitance of circuit.

Now, when inductance and capacitance changes, i.e., ${L}^{'} = 2L$ and ${C}^{'} = 8C$

Then, resonant frequency is $\omega = \dfrac{1}{\sqrt{2L \times 8C}} = \dfrac{1}{4\sqrt{LC}}$

$⇒ \omega = \dfrac{{\omega}_{0}}{4}$

Thus, the value of $x = \dfrac{1}{4}$.