An AC circuit has an inductor and a resistor of resistance R in...

First Recall the formula of power factor, $cosϕ = \dfrac{R}{Z}$$⇒ cos{ϕ}_{initial} = \dfrac{R}{Z} = \dfrac{R}{\sqrt{{\left({X}_{L}\right)}^{2} + {R}^{2}}} = \dfrac{R}{\sqrt{9{R}^{2} + {R}^{2}}} = \dfrac{1}{\sqrt{10}}$.

$⇒ cos{ϕ}_{final} = \dfrac{R}{Z} = \dfrac{R}{\sqrt{{\left({X}_{L} - {X}_{C}\right)}^{2} + {R}^{2}}} = \dfrac{R}{\sqrt{{R}^{2} + {R}^{2}}} = \dfrac{1}{\sqrt{2}}$

$⇒ \dfrac{cos{ϕ}_{final}}{cos{ϕ}_{initial}} = \dfrac{\sqrt{5}}{x} ⇒ x = 1$