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Question Number 119408 by ZiYangLee last updated on 24/Oct/20
Ifα,β,γarethethreerootsofthe3x3+12x2−77x+11=0,findthevalueof(α−1)(β−1)(γ−1).
Commented by liberty last updated on 24/Oct/20
letp(x)=3x3+12x2−77x+11andp(x)=0hastherootsareα,βandγletp(x+1)=3(x+1)3+12(x+1)2−77(x+1)+11hastherootsare{α−1β−1γ−1p(x+1)=3(x3+3x2+3x+1)+12(x2+2x+1)−77x−77+11p(X)=3x3+21x2−44x−51thus(α−1)(β−1)(γ−1)=513=17
Answered by mr W last updated on 24/Oct/20
α+β+γ=−123αβ+βγ+γα=−773αβγ=−113(α−1)(β−1)(γ−1)=αβγ+(α+β+γ)−(αβ+βγ+γα)−1=−113−123+773−1=17
Commented by ZiYangLee last updated on 24/Oct/20
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