Câu hỏi 5
Cho các số dương $x_1,x_2,\ldots,x_n$, với $n\geq2$. Chứng minh rằng
$$
\left(x_1+\frac1{x_1}\right)\left(x_2+\frac1{x_2}\right)\cdots\left(x_n+\frac1{x_n}\right)\geq\left(x_1+\frac1{x_2}\right)\left(x_2+\frac1{x_3}\right)\cdots\left(x_{n-1}+\frac1{x_n}\right)\left(x_n+\frac1{x_1}\right).
$$
$$
\left(x_1+\frac1{x_1}\right)\left(x_2+\frac1{x_2}\right)\cdots\left(x_n+\frac1{x_n}\right)\geq\left(x_1+\frac1{x_2}\right)\left(x_2+\frac1{x_3}\right)\cdots\left(x_{n-1}+\frac1{x_n}\right)\left(x_n+\frac1{x_1}\right).
$$