《数学通报》2013年第7期第2134号数学问题引起广泛关注,其中安振平老师在他的博客[5]中对该问题有多种有别于本刊[1]的证明.特别罗列了张云华、熊昌进老师的独立证明.本人也学习了这些老师的解答,并参考了相应文献,有体会如下.问题a,b,c是满足(a+b+c-2)~2=2abc的任意实数,求证:(1-a)(1-b)(1-c)≤1/8.证明设1-a=x,1-b=y,1-c=z,则原 The mathematics problem of No. 2134 in 2013 No. 7 of 2013 is widely concerned, of which Mr. An Zhenping has a lot of different proofs on this issue in his blog [5]. [1] Zhang Yunhua, Xiong Changjin independent proof of the teacher. I also studied the answers of these teachers, and with reference to the corresponding literature, as follows. Question a, b, c is to meet the (a + b + c-2) ~ 2 = 2abc Arbitrary real numbers, prove: (1-a) (1-b) (1-c) ≤ 1/8 Proof Let 1-a = x, 1-b = y, 1-c =