Multiple choice

If $p, q, r$ are the roots of the cubic equation $x^3-3x+4=0$, then value of $\dfrac{1}{p^3+q^3+8}+\dfrac{1}{q^3+r^3+8}+\dfrac{1}{r^3+p^3+8}$ is equal to

  1. maximum value of $f(x)=-x^2+2x-\frac{1}{4}\forall x\in \begin{bmatrix}
    -2,2
    \end{bmatrix}$
  2. minimum value of $g(x)=2x^2-3x+\frac{7}{8}\forall x\in \begin{bmatrix}
    -1,1
    \end{bmatrix}$
  3. $-\frac{1}{\alpha }$ where $\alpha $ is characteristic of $\log_9(6569)$
  4. value of $\log_{(antilog_{128}\left(\frac{4}{7}\right)}\left(\dfrac {1}{2}\right)$
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