一、忽略区间端点致误例1已知关于x的不等式ax-5x2-a0的解集为M,若3∈M且5M,求实数a的取值范围.错解由3∈M且5M得3a-59-a0,且5a-525-a≥0.这等价于不等式组(a-53)(a-9)0,(a-1)(a-25)≤0且a≠25 解得a∈犤1,53)∪(9,25).剖析因为当a=25时,x=5恰好不是25x-5x2-250的解,即5M 1. Ignoring Interval Endpoint Error Example 1 Given that the solution set of ax-5x2-a0 on x is M, if 3∈M and 5M, the range of value of a is a. The wrong solution is obtained from 3∈M and 5M. 3a-59-a0, and 5a-525-a ≥ 0. This is equivalent to the inequality group (a-53)(a-9)0, (a-1) (a-25) ≤ 0 and the a≠25 solution Dea 1,53) ∪ (9,25). Because when a=25, x=5 is not a solution of 25x-5x2-250, ie 5M