Question 25
Let $x_{1}, x_{2}, \ldots, x_{n}$ be positive real numbers for which
$$
\frac{1}{1+x_{1}}+\frac{1}{1+x_{2}}+\ldots+\frac{1}{1+x_{n}}=1
$$
Prove that
$$
x_{1} x_{2} \ldots x_{n} \geq (n-1)^{n}
$$
$$
\frac{1}{1+x_{1}}+\frac{1}{1+x_{2}}+\ldots+\frac{1}{1+x_{n}}=1
$$
Prove that
$$
x_{1} x_{2} \ldots x_{n} \geq (n-1)^{n}
$$