\(P=\frac{a+b}{abc}=\frac{1}{c}\left(\frac{a+b}{ab}\right)=\frac{1}{1-\left(a+b\right)}.\left(\frac{1}{a}+\frac{1}{b}\right)\ge\frac{1}{\left(1-2\sqrt{ab}\right)}.\frac{2}{\sqrt{ab}}\)
\(P\ge\frac{4}{\left(1-2\sqrt{ab}\right).2\sqrt{ab}}\ge\frac{4}{\frac{\left(1-2\sqrt{ab}+2\sqrt{ab}\right)^2}{4}}=16\)
\(\Rightarrow P_{min}=16\) khi \(\left\{{}\begin{matrix}a=b=\frac{1}{4}\\c=\frac{1}{2}\end{matrix}\right.\)
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