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  • If alpha , beta , gamma are the roots of p,q<0 , then for any x,y and z the expression x(alpha)+y(beta) +z(gamma)/x(beta)+y(gamma)+z(alpha) equals.

If alpha , beta , gamma are the roots of p,q<0 , then for any x,y and z the expression x(alpha)+y(beta) +z(gamma)/x(beta)+y(gamma)+z(alpha) equals.

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Solution:      x^3=p=(p^1/3)^3Rightarrow x=p^1/3,p^1/3omega ,p^1/3omega ^2

                Let     alpha =p^1/3   ,  eta =p^1/3hspace0.1cmomega  ,  gamma =p^1/3hspace0.1cmomega ^2

            Rightarrow            xalpha +yeta +zgamma /xeta +ygamma +zalpha =x+yomega +omega ^2z/xomega +yomega ^2+z=(1/omega )=omega ^2

 

Posted by

Deependra Verma

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