2004西部数学奥林匹克试题第三题为:求所有的实数k,使得不等式a2+b2+c2+d2+1≥k(a+b+c+d)对任意a,b,c,d∈[-1,+∞)都成立。文[1]给出它的解为k=34,从而上题可改叙如下:定理1对于任意a,b,c,d∈[-1,+∞),有a3+b3+c3+d3+1≥34(a+b+c+d)。证明见文[1]。进一步研究,又可得到如下的几 The third question in the 2004 Western Mathematical Olympiad is to find all real numbers k such that the inequality a2 + b2 + c2 + d2 + 1 ≥ k (a + b + c + d) 1, + ∞) are valid. The solution given in [1] is k = 34, so that the above problem can be reclassified as follows: Theorem 1 For any a, b, c, d∈ [-1, + ∞), there is a3 + b3 + c3 + d3 + 1 ≧ 34 (a + b + c + d). Proof see article [1]. Further research, but also get the following few