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众所周知,求分式函数y=ax~2+bx+c/lx~2+mx+n(a、l不同时为零)的值域,可用判别式法。但如果给自变量x以一定的限制,就不能用这一方法,一般须用导数来求解。本文介绍一种比较简便的初等方法。我们知道,关于一元二次方程的实根分布有以下结论:设f(x)=x~2+px+q,则 1.方程f(x)=0在区间(m,+∞)内有根的充要条件为(若把区间(m,+∞)改为[m,+∞),则把前一条件改为f(m)≤0)。 2.方程f(x)=0在区间(m,n)内有根的充要条件为
It is well known that the fractional function y=ax~2+bx+c/lx~2+mx+n (a and l are not zero at the same time) can be found by the discriminant method. However, if there is a certain limit to the independent variable x, this method cannot be used, and it is generally necessary to use a derivative to solve it. This article describes a relatively simple elementary method. We know that the real root distribution of quadratic equations has the following conclusion: Let f(x) = x~2+px+q, then 1. The equation f(x) = 0 in the interval (m, +∞) The necessary and sufficient condition of the root is (if the interval (m, + ∞) is changed to [m, + ∞), the previous condition is changed to f (m) ≤ 0). The necessary and sufficient condition for the root of the equation f(x)=0 in the interval (m,n) is