If α,β and γ are the roots of the equation x3 + 3x2 + 5x - 6 = 0, find the value of (α−1βγ)(β−1γα)(γ−1αβ)(1α+1β+1γ)−1
256
α,β and γ are the roots of the equation x3 + 3x2 + 5x - 6 = 0
As we know,
α+β+γ=−ba=−3,
αβ+βγ+γα=5,
αβγ=−da=6
Here,
(α−1βγ)(β−1γα)(γ−1αβ)(1α+1β+1γ)−1
=(α−1βγ)(β−γγa)(γ−1αβ)(αβγαβ+βγ+γα)=(αβγ−1)(αβγ−1)(αβγ−1)α2β2γ2×αβγ(αβ+βγ+γα)
=(αβγ−1)3αβγ(αβ+βγ+γα)=536×5=256