RMO practice question 7

Algebra Level 5

Let a,b,ca,b,c be the roots of x39x2+11x1=0x^{3}-9x^{2}+11x-1=0 and ω=a+b+cω=\sqrt{a}+\sqrt{b}+\sqrt{c} , the find the value of ω418ω28ω+40.ω^{4}-18ω^{2}-8ω+40.

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