构造二次函数,然后利用二次函数的性质来证明不等式,这种方法的推导论证过程比较严谨,可避免出现由于放缩不当而导致放得过大或缩得过小的麻烦。兹举几例说明如下: 例1 设a、b、c∈R~+,abc=1,则a~2+b~2+c~2+3≥2ab+2ac+2bc。 评析:许多人尝试用基本不等式进行放缩或通过换元去解决这个问题,都没能如愿。若 Construct a quadratic function, and then use the properties of the quadratic function to prove the inequality. The derivation process of this method is more rigorous, and it can avoid the trouble of too large or too small due to improper scaling. Here are a few examples to illustrate: Example 1 Let a, b, c∈R~+,abc=1, then a~2+b~2+c~2+3≥2ab+2ac+2bc. Comment: Many people try to use the basic inequality to scale or solve the problem by replacing the yuan, they failed to do so. If