近两年,在众多刊物上,载有不等式: multiply from i=1 to n(x_i+1/x_i)≥(λ/n+n/λ) (*)这里x_i∈R~+(i=1,2,…,n),x_1+x_2+…+x_n=λ≤n,仅当x_1=x_2=…=x_n时(*)式取等号。现在,我们给出(*)的一个加强: 定理设x_i∈R~+(i=1,2,…,n,n≥2),且sum from i=1 to n x_i=λ(常数)≤n,则 sum from i=1 to n(x_i+1/x_i)~(-1)≤n(λ/n+n/λ)~(-1) (1)当且仅当x_1=x_2+…=x_n时,(1)式中的等号成立。 In the past two years, in many publications, there is an inequality: multiply from i=1 to n(x_i+1/x_i)≥(λ/n+n/λ) (*) where x_i∈R~+(i=1 ,2,...,n),x_1+x_2+...+x_n=λ≤n, only when x_1=x_2=...=x_n (*) takes the equal sign. Now we give a (*) reinforcement: The theorem sets x_i∈R~+(i=1,2,...,n,n≥2), and sum from i=1 to n x_i=λ(constant)≤ n, then sum from i=1 to n(x_i+1/x_i)~(-1)≤n(λ/n+n/λ)~(-1) (1) If and only if x_1=x_2+...= When x_n, the equal sign in (1) holds.