<s>[INST] Given that $a^2(a+k)=b^2(b+k)=c^2(c+k)$, find the value of $1/a+1/b+1/c$ 
Given $$a^2(a+k)=b^2(b+k)=c^2(c+k)$$
  find the value of $1/a+1/b+1/c$.

I tried to derive a relation from the equality but it did not help my cause. 
 [/INST] HINT:
Let $$a^2(a+k)=b^2(b+k)=c^2(c+k)=d$$
So $a,b,c$ are the roots of $x^3+x^2k-d=0$
Using Vieta's Formula, $a+b+c=-k, ab+bc+ca=0,abc=d$
$$\text{Now,}\frac1a+\frac1b+\frac1c=\frac{ab+bc+ca}{abc}$$
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