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RMO type algebra practice question

Question: Show that the following expression $latex [4-3x+ \sqrt{16+9x^{2}-24x-x^{3}}]^{1/3}+ [4-3x-\sqrt{16+9x^{2}-24x-x^{3}}]^{1/3}$ remains constant in the interval $latex 0 \leq x \leq 1$. Find…