From the binomial theorem, the coefficient of $x$ is $\binom{n}{1}(1/k)$ and the coefficient of $x^2$ is $\binom{n}{2}(1/k)^2$. This creates a system in $n$ and $k$ you can solve.
clever badger
From the binomial theorem, the coefficient of $x$ is $\binom{n}{1}(1/k)$ and the coefficient of $x^2$ is $\binom{n}{2}(1/k)^2$. This creates a system in $n$ and $k$ you can solve.
hard yachtBOT
Civil Service Pigeon
clever badger
Expand out the coefficients, which gives $n$ in terms of $k$ (or vice versa) for the first equation, which you can substitute into the second equation.