If `alpha, beta` are the roots fo the equation `lamda(x^(2)-x)+x+5=0`. If `lamda_(1)` and `lamda_(2)` are two values of `lamda` for which the roots `alpha, beta` are related by `(alpha)/(beta)+(beta)/(alpha)=4/5` find the value of `(lamda_(1))/(lamda_(2))+(lamda_(2))/(lamda_(1))`

Explanation

To solve the problem, we start with the given equation:

\[ \lambda (x^2 - x) + x + 5 = 0 \]

We can rearrange this equation as:

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