Obviously the energy transfered from capacitor is accumulated in inductor so:
[tex] W_C = W_L [/tex]
If we assume that inductor is discharged in the instant [tex]t_1[/tex] then [tex]i(t_1) = 0[/tex], and capacitor is charged to the volgate [tex]v(t_1) = V[/tex]. Assume that the capacitor is discharged in in [tex]t_2[/tex] instant. From the energy ballance we get the current:
[tex]i(t_2) = \sqrt{\frac{C}{L}} V[/tex]
Which is obviously different than 0. From this observation you get the answer to your question.