换元法是证明含条件不等式的一种常用方法。通过换元可以创造条件,较快地使问题得到解决。但究竟怎样由题设条件,恰当而巧妙地进行换元呢?根据笔者的体会,本文列举了八种方法(为了归类与帮助记忆,由各种不同换元法的特点,都给予其相应的名称),供证明此类问题时作参考。 (一)对称假设法当已知条件是两元素(项)之和为常数2k时则可考虑设一个元素(项)为k+h,另一个元素(项)为k-h,再代入所求证的不等式。特别是证明当字母具有对称性的不等式时,此法更显示出它的优越性。例1 已知a+b=2k (k为常数),求证a~4+b~4≥2k~4. The substitution method is a common method to prove the conditional inequality. You can create conditions by replacing the element and solve the problem faster. But how exactly does the subject set up the conditions and do it appropriately and skillfully? According to the author’s experience, this article enumerates eight methods (for classifying and assisting memory, the characteristics of various alternatives are given The name) is for reference when proving such issues. (a) Symmetrical hypothesis When the known condition is that the sum of two elements (items) is a constant 2k, consider setting an element (item) to k+h and another element (item) to kh, and substituting it for verification. inequality. In particular, it is proved that this method shows its superiority when the letters have symmetry inequalities. Example 1 It is known that a+b=2k (k is a constant). Prove that a~4+b~4≥2k~4.