Let \(\alpha=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 …

Let \(\alpha=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\). If \(8 x^2+b x+c=0\) is a quadratic equation whose roots are \(\alpha^{1 / 5}\) and \(\beta^{1 / 5}\), then the value of \(c-b\) is equal to:

[JEE Main 2021, 27 Jul (Shift 2)]