Cho các số nguyên a,b,c khác 0 thoả mãn:
$\left\{\begin{matrix} \frac{a}{b}+\frac{b}{c}+\frac{c}{a}\epsilon Z\\\frac{a}{c}+\frac{b}{a}+\frac{c}{b}\epsilon Z \\ \end{matrix}\right.$
Chứng minh rằng: $\frac{3a^{4}}{b^{2}}+\frac{2b^{4}}{c^{2}}+\frac{c^{4}}{a^{2}}-4\begin{vmatrix} a \end{vmatrix}-3\begin{vmatrix} b \end{vmatrix}-2\begin{vmatrix} c \end{vmatrix}\geqslant 0$
