Triple System of Equations

Algebra Level 3

α+β+γ=6α3+β3+γ3=87(α+1)(β+1)(γ+1)=33\large \begin{aligned}\alpha+\beta+\gamma&=6 \\\alpha^3+\beta^3+\gamma^3&=87\\ (\alpha+1)(\beta+1)(\gamma+1)&=33 \end{aligned}

Suppose α\alpha, β\beta, and γ\gamma are complex numbers that satisfy the system of equations above.

If 1α+1β+1γ=mn\frac1\alpha+\frac1\beta+\frac1\gamma=\tfrac mn for positive coprime integers mm and nn, find m+nm+n.

×

Problem Loading...

Note Loading...

Set Loading...