If $x^3 +px -q =0$ then value of $(\alpha + \beta)(\beta + \gamma)(\alpha+\gamma)(1/\alpha^2 + 1/\beta^2+1/\gamma^2)$ I am given a cubic equation $E_1 : x^3 +px -q =0$ where $p,q \in R$ so what would be value of the expression  $$(\alpha + \beta)(\beta + \gamma)(\alpha+\gamma)(\frac{1}{\alpha^2} + \frac{1}{\beta^2}+\frac{1}{\gamma^2})$$ where $\alpha , \beta,\gamma$ are roots of cubic equation $E_1$
I know that this has got to do something with sum/product of root of equation but I don't know how to solve this problem , perhaps I can do something by assuming value of $p,q$ to be something then solve the given expression?

hint: do you see that $ \alpha \beta +\beta \gamma+ \gamma \alpha = p $ and $\alpha \beta \gamma = q$?
