Lời giải:
Do $a,b,c\leq 2\Rightarrow a-2\leq 0; b-2\leq 0; c-2\leq 0$
$\Rightarrow (a-2)(b-2)(c-2)\leq 0$
\(\Leftrightarrow (ab-2a-2b+4)(c-2)\leq 0\)
\(\Leftrightarrow abc-2(ab+bc+ac)+4(a+b+c)-8\leq 0\)
\(\Leftrightarrow 2(a+b+c)-(ab+bc+ac)+\frac{abc}{2}\leq 4\)
Mà $abc\geq 0$ do $a,b,c\geq 0$
\(\Rightarrow 4\geq 2(a+b+c)-(ab+bc+ac)+\frac{abc}{2}\geq 2(a+b+c)-(ab+bc+ac)\)
Ta có đpcm.