Answer to Question #75451 in Algebra for Rajni

Question

Let x_i belongs to R such that 0 < x_1<= x_2 <= ...<= x_n , n>= 2 and (1/1+x_1)+(1/1+x_2)+...+(1/1+x_n) = 1 .Then show that √x_1 + √x_2 + ..+ √x_n >= (n-1) [( 1/√x_1)+...+(1/√x_n) .