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已知tanα,tanβ是关于x的方程mx~2+7m-3x~(1/2)+2m=0的两个实根,求tan(α+β)的最大值.这道题以三角函数为载体,涉及求函数最值的几种典型的方法和策略,非常值得探究,主要有以下五种解法:由韦达定理,得到
It is known that tan α is the maximum value of tan (α + β) for two real roots of the equation mx ~ 2 + 7m-3x ~ (1/2) + 2m = 0 for x. This problem is solved by a trigonometric function As a carrier, several typical methods and strategies involving seeking the most value of the function are worth exploring. There are mainly five solutions: From the Vedic theorem, we get