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将x+y=m中的x、y分别用m/2+t、m/2-t来代换,这种代换通常称为均值代换.用均值代换解一些最值竞赛题可以简化解题步骤,收到理想的解题效果.下面举例予以说明,供中学师生参考.例1已知a,b,c,d,e是满足a+b+c+d+e=8,a~2+b~2+c~2+d~2+e~2=16的实数,试求e的最大值和最小值.(第7届美国数学奥林匹克试题)
Substituting x and y in x + y = m for m / 2 + t and m / 2-t, respectively, this substitution is usually called mean substitution. A, b, c, d, e is a + b + c + d + e = 8 which is known to be suitable for secondary school teachers and students. , a ~ 2 + b ~ 2 + c ~ 2 + d ~ 2 + e ~ 2 = 16 real number, try to find the maximum and minimum e. (7th American Mathematical Olympiad)