Inequality on Quotient Substution and Cauchy

1. Let $n>3$ and for positive $x_1,...,x_n$, and $x_1x_2...x_n=1$. Prove that: $1/(1+x_1+x_1x_2)+...+1/(1+x_n+x_nx_1)>1$

For this inequality I do not see how to prove it using the conditions that their product is one.

1. Let $a,b,c,x,y,z\geq 0$, show that $(b+c)x+(c+a)y+(a+b)z\geq 2\sqrt{(xy+yz+xz)(ab+bc+ac)}$
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