Answer to Question #78460 in Algebra for DK

Question

Let xi ∈ R such that 0 < x1 ≤ x2 ≤ .....≤ xn,
n ≥ 2, and 1/(1+x1) + 1/(1+x2) +........+1/(1+xn) =1 then show that
√x1 + √x2 +........+ √xn ≥ (n-1) {1/√x1 + .....+ 1/√xn}