Easy one .

Algebra Level 4

lf α\displaystyle\alpha and β\displaystyle\beta are the roots of the equation λ(x2+x)+x+5=0,\displaystyle\lambda (x^{2} +x) +x+5=0, and λ1\displaystyle\lambda_{1} and λ2\displaystyle\lambda_{2} are two values of λ\displaystyle\lambda for which α\displaystyle\alpha , β\displaystyle\beta are connected by the relation αβ+βα=4,\displaystyle\frac{\alpha}{\beta}+\frac{\beta}{\alpha} =4 , then what is the value of λ1λ2+λ2λ1?\displaystyle\frac{\lambda_{1}}{\lambda_{2}}+\frac{\lambda_{2}}{\lambda_{1}} ?

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