If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^{3}+4x+2=0$,then $\alpha^{3}+\beta^{3}+\gamma^{3}$ is equal to

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 35x + 2 = 0$,then the value of $(2\alpha - 35)^3 \cdot (2\beta - 35)^3$ is equal to

Let $a$ be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation $x^3 - ax^2 + ax - 1 = 0$ is identical to the original cubic equation,then $a =$

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+ax^2+bx+c=0$,then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}$ is equal to

If one root of the quadratic equation $ax^2 + bx + c = 0$ is equal to the $n$th power of the other,then $(ac^n)^{1/(n+1)} + (a^nc)^{1/(n+1)} =$