Let x1,x2,…,xn be positive real numbers and xn+1=x1+x2+⋯+xn. Prove that n∑k=1√xk(xn+1−xk)≤√n∑k=1xn+1(xn+1−xk). Mircea Becheanu
Problem
Source: Romanian IMO Team Selection Test TST 1996, problem 13
Tags: inequalities, inequalities proposed
Source: Romanian IMO Team Selection Test TST 1996, problem 13
Tags: inequalities, inequalities proposed
Let x1,x2,…,xn be positive real numbers and xn+1=x1+x2+⋯+xn. Prove that n∑k=1√xk(xn+1−xk)≤√n∑k=1xn+1(xn+1−xk). Mircea Becheanu