RMO practice question 7

Algebra Level 5

Let \(a,b,c\) be the roots of \(x^{3}-9x^{2}+11x-1=0\) and \(ω=\sqrt{a}+\sqrt{b}+\sqrt{c}\) , the find the value of \[ω^{4}-18ω^{2}-8ω+40.\]

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