Given nonnegative real numbers x1,x2,…,xn, let a=min{x1,x2,…,xn}. Prove that the following inequality holds:
\sum^{n}_{i=1}\dfrac{1+x_i}{1+x_{i+1}}\le n+\dfrac{1}{(1+a)^2}\sum^{n}_{i=1}(x_i-a)^2 (x_{n+1}=x_1),
and equality occurs if and only if x1=x2=⋯=xn. inequalitiesquadraticsinequalities unsolved