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  • If ? and ? are the roots of the equation x²-p(x+1)-q=0 then find the value of (?²+2?+1/?²+2?+q)+(?²+2?+1/?²+2?+q)

If ? and ? are the roots of the equation x²-p(x+1)-q=0 then find the value of (?²+2?+1/?²+2?+q)+(?²+2?+1/?²+2?+q)

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x^2-p(x-1)-q=0\*Rightarrow x^2-px-(p+q)=0\*It;has;alpha ;and;eta;as;roots;so,\*alpha+eta=p;and;alpha eta=-(p+q)\* Rightarrow alpha+eta+alphaeta=p-p-q=-q\*fracalpha^2+2alpha+1alpha^2+2alpha+q+ fraceta^2+2eta+1eta^2+2eta+q=?\* fracalpha^2+2alpha+1alpha^2+2alpha-alpha-eta-alphaeta+fraceta^2+2eta+1eta^2+2eta-alpha-eta-alphaeta\* frac(alpha+1)^2(alpha-eta)(alpha+1)+frac(eta+1)^2(eta-alpha)(eta+1)\* fracalpha+1alpha-eta-fraceta+1alpha-eta=fracalpha-eta+1-1alpha-eta=fracalpha-etaalpha-eta=1

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Deependra Verma

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