Ta có: \(\left\{{}\begin{matrix}a\le1\\b\le1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a-1\le0\\b-1\le0\end{matrix}\right.\Rightarrow\left(a-1\right)\left(b-1\right)\ge0\)
\(\Rightarrow a\left(b-1\right)-\left(b-1\right)\ge0\)
\(\Rightarrow ab-a-b+1\ge0\)
\(\Rightarrow ab+1\ge a+b\)
Dấu \("="\) xảy ra khi: \(\left\{{}\begin{matrix}a=1\\b=1\end{matrix}\right.\)
$\text{#}Toru$