我们知道,不等式ax2+bx+c>0(a≠0) 在实数集R上恒成立的充要条件是a>0且△ =b2-4ac<0．如果把结论稍加扩展:不等式左 边的表达式不一定是关于x的二次三项式,给 自定区间不是实数集R而是实数集R的子集,依 然讨论使不等式恒成立的条件,内容就丰富得 多了,我们姑且把它称为“不等式恒成立”问题． 这类问题在近几年高考数学中已多次出现． We know that the necessary and sufficient condition for the inequality ax2+bx+c>0(a≠0) to be constant on the real set R is a>0 and △=b2-4ac<0. If we slightly expand the conclusion: the expression on the left side of the inequality does not have to be about the quadratic trinomial of x, and given that the self-defined interval is not a subset of a real set R but a set of real numbers R, we still discuss the conditions that make the inequality constant. The content is much richer, and we will call it “inequality constant” problem. This kind of problem has appeared many times in the mathematics of college entrance examination in recent years.