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Multiple choice

If $\alpha, \beta, \gamma$ are roots of equation $x^3-3x^2+5x-k=0$ such that $\alpha\left(\dfrac{1}{\beta}+\dfrac{1}{\gamma}\right)+\beta\left(\dfrac{1}{\alpha}+\dfrac{1}{\gamma}\right)+\gamma\left(\dfrac{1}{\beta}+\dfrac{1}{\alpha}\right)=2$ then value of k is?

  1. $6$
  2. $-9$
  3. $3$
  4. $9$
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