HMMT 2006 A6

Let $a, b, c$ be the roots of $x^{3}-9 x^{2}+11 x-1=0$ , and let $s=\sqrt{a}+\sqrt{b}+\sqrt{c}$ . Find $s^{4}-18 s^{2}-8 s$ .

Dataset text NuminaMath olympiads. Quoted with source.

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