Solution
= Solution
For $\beta\in K$, the nonzero algebraic number $\gamma=\alpha-\beta$ has degree at most
$$
[\mathbb Q(\alpha,\beta):\mathbb Q]\leq3\cdot2=6.
$$
The basic height inequality gives
$$
H(\gamma)\leq2H(\alpha)H(\beta).
$$
The <Liouville height inequality> therefore yields
$$
|\alpha-\beta|
\geq H(\gamma)^{-6}
\geq(2H(\alpha))^{-6}H(\beta)^{-6}.
$$
Thus one may take the explicit constant
$$
c=(2H(\alpha))^{-6}.
$$