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均值不等式是求解最值、证明不等式的常用工具,其中“正”、“定”、“等”是该不等式应用的三个原则,而构造定值是应用的关键,特别对于存在多个变量的不等式问题,本文对多元均值不等式的构造策略举例探究如下。策略一:整体性原则例1已知正实数x,y满足xy+2x+y=4,则x+y的最小值为_________。思路分析:本题所求表达式x+y刚好在条件中有所体现,所以
Means inequality is a common tool to solve the most value and prove inequality, among which “正 ”, “definite ”, “etc. ” are the three principles of the inequality applied, and the construction of fixed value is the key to application, especially For inequality with multiple variables, this paper explores the construction strategy of multivariate mean inequality as follows. Strategy One: The Principle of Holisticness Example 1 Known positive real number x, y satisfies xy + 2x + y = 4, the minimum value of x + y is _________. Analysis of ideas: The expression of the problem x + y just reflected in the conditions, so