RMO type algebra practice question

Question:

Show that the following expression

$[4-3x+ \sqrt{16+9x^{2}-24x-x^{3}}]^{1/3}+ [4-3x-\sqrt{16+9x^{2}-24x-x^{3}}]^{1/3}$

remains constant in the interval $0 \leq x \leq 1$. Find this constant value.

Answer will be posted later.

Nalin Pithwa.

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