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一、与二次不等式有关的恒成立问题任何一个一元二次不等式总可以化成 ax~2+bx+c>O (a>O) ax~2+bx+c0)的形式,由二次函数y=ax~2+bx+c(a>0)的图象和性质,我们不难得出以下两个结论: (i)ax~2+bx+c>0 (a>0)在区间[α,β]上恒成立的充要条件是特别地,若a取-∞或β取+∞,则其充要条件只要改为去掉含∫(α)或∫(β)的不等式就是。若α取-∞同时β取+∞,则其充要条件只要去掉第二组不等式就是,即
1. The constant establishment problem associated with quadratic inequalities Any single quadric inequality can always be in the form of ax~2+bx+c>O (a>O) ax~2+bx+c0) From the image and properties of the quadratic function y=ax~2+bx+c(a>0), we can easily draw the following two conclusions: (i)ax~2+bx+c>0 (a>0 The necessary and sufficient condition for the constant establishment in the interval [α,β] is, in particular, if a takes -∞ or β takes +∞, its necessary and sufficient conditions need only be replaced by removing the ∫(α) or ∫(β). Inequality is. If α takes -∞ and β takes +∞, the necessary and sufficient condition is that if we remove the second group inequality, that is,