<s>[INST] AM-GM Inequality concept challenged! If $a,b,c$ are positive numbers and $abc=9$, then find the minimum value of $(1+a)(1+b)(1+c)=?$
Someone's approach is  
but for this to be possible, $a=b=c=1$. which doesn't satisfies $abc=9$.
Where does the above method go wrong and what should be the correct answer?
 [/INST] By AM-GM
\begin{align}
1+a &\geq 2 \sqrt{a} \\
1+b &\geq 2 \sqrt{b} \\
1+c &\geq 2 \sqrt{c} 
\end{align}
Thus
\begin{align}
(1+a)(1+b)(1+c) &\geq 2^3 \sqrt{a} \sqrt{b}\sqrt{c} \\
&= 8.\sqrt{9} \ldots
\end{align}
Can you take it from here?
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