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If α,β,ȣ are the roots of equation x3–3x2+3x+7=0 and ω is cube root of unity, then evaluate (α-1)/(β-1)+(β-1)/(ȣ-1)+(ȣ-1)/(α-1).

If α,β,ȣ are the roots of equation x3–3x2+3x+7=0 and ω is cube root of unity, then evaluate (α-1)/(β-1)+(β-1)/(ȣ-1)+(ȣ-1)/(α-1). Correct Answer 3ω2

equation can be simplified to (x-1)3=-8⇒(x-1)/(-2)=(1)1/3⇒roots: 1,ω,ω2 ⇒ α=-1, β=1-2ω, ȣ=1-2ω2. Therefore, required value=-2/(-2ω)+(-2ω)/(-2ω2)+(-2ω2)/(-2) = 1/ω+1/ω+1/ω=3/ω=3ω2.

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