C h o $a,\,b,\,c\geqq 3$ $,$ c h ứ n g m i n h
$$\begin{equation}\begin{split} 3(\,abc+ b+ 2\,c\,)\geqq 2(\,ab+ 2\,ac+ 3\,bc\,) \end{split}\end{equation}$$
$\lceil$ Malaysia Jr $\it{2015}$ $\rfloor$
P h é p t h ế R a v i
$$\begin{equation}\begin{split} a= 3+ A,\quad b=3+ B,\quad c= 3+ C \quad \left [ A,\quad B,\quad C\geqq\quad 0 \right ] \end{split}\end{equation}$$
B à i t o á n t r ở t h à n h
$$\begin{equation}\begin{split} P= 3\,ABC+ 7\,AB+ 3\,BC+ 5\,CA+ 9\,A+ 6\,B+ 3\,C\quad \left [ \quad P= (\,3bc- 2\,b- 4\,c\,)a+ 3\,b+ 6\,c- 6\,abc \quad \right ] \end{split}\end{equation}$$
C h ẳ n g h ạ n
N h ờ t h a y đ ổ i h ệ s ố
$$\begin{equation}\begin{split} 0\leqq 1\,ABC+ 2\,AB+ 3\,BC+ 4\,CA+ 5\,A+ 6\,B+ 7\,C \end{split}\end{equation}$$
T r ở t h à n h b à i t o á n
$$\begin{equation}\begin{split} abc+ ac\geqq 4\,a+ ab+ 5\,c \end{split}\end{equation}$$
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