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Soient \(a,b,c\) les racines de \(X^3 + pX + q\), \(q \ne 0\). Calculer : \(\sum_{\sigma \in S_3} \left( \frac {\sigma(a)}{\sigma(b)} + \frac {\sigma(b)}{\sigma(c)} + \frac {\sigma(c)}{\sigma(a)} \right)\).
Soient \(a,b,c\) les racines de \(X^3 + pX + q\), \(q \ne 0\). Calculer : \(\sum_{\sigma \in S_3} \left( \frac {\sigma(a)}{\sigma(b)} + \frac {\sigma(b)}{\sigma(c)} + \frac {\sigma(c)}{\sigma(a)} \right)\).