解数学题,遇到形如x+y=2a的条件,可设x=a+k,y=a-k(k是参数),从而有效地解决许多类型的题,这就是均值换元,本文介绍用此法在解题中的应用。1、用于条件求值。例1若a+b=5,a3+b3=50,求a2+b2解:设a=52+k,b=52-k∴(52+k)3+(52-k)3=50,即(52+k+52-k)[(52+k)2-(52+k)(52-k)+(52-k)2]=5 Solve mathematics problems, meet the conditions such as x + y = 2a, can be set x = a + k, y = ak (k is a parameter), which effectively solve many types of questions, which is the average value of yuan, this article describes Use this method in solving problems. 1, for conditional evaluation. Example 1 If a+b=5 and a3+b3=50, find a2+b2 solution: Let a=52+k, b=52-k∴(52+k)3+(52-k)3=50, That is, (52+k+52-k)[(52+k)2-(52+k)(52-k)+(52-k)2]=5