6. Let $n \geq 3$ be an integer, and let $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ be variables which take real values with $0 \leq x _ { i } \leq 1$ for all $1 \leq i \leq n$. Let $$\begin{aligned}
A & = x _ { 1 } + x _ { 2 } + \ldots + x _ { n } \\
B & = x _ { 1 } x _ { 2 } + x _ { 2 } x _ { 3 } + \ldots + x _ { n - 1 } x _ { n } + x _ { n } x _ { 1 }
\end{aligned}$$ Which of the following statements is/are true. (a) $A \geq B$ is always true. (b) $B > A$ is true for some values of the $x _ { i }$ 's and $A > B$ is true for some values of the $x _ { i }$ 's. (c) $A = B$ has a finite number of solutions (d) $A = B$ has an infinite number of solutions.
6. Let $n \geq 3$ be an integer, and let $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ be variables which take real values with $0 \leq x _ { i } \leq 1$ for all $1 \leq i \leq n$. Let
$$\begin{aligned}
A & = x _ { 1 } + x _ { 2 } + \ldots + x _ { n } \\
B & = x _ { 1 } x _ { 2 } + x _ { 2 } x _ { 3 } + \ldots + x _ { n - 1 } x _ { n } + x _ { n } x _ { 1 }
\end{aligned}$$
Which of the following statements is/are true.\\
(a) $A \geq B$ is always true.\\
(b) $B > A$ is true for some values of the $x _ { i }$ 's and $A > B$ is true for some values of the $x _ { i }$ 's.\\
(c) $A = B$ has a finite number of solutions\\
(d) $A = B$ has an infinite number of solutions.\\