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^…

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 \( a^{1 / 5} \) and \( \beta^{1 / 5} \), then the value of \( c-b \) is equal to

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