摘要：19．设全集I＝R.A＝{x|x2-2x＞0.x∈R}.B＝{x|x2-ax+b＜0.x∈R}.C＝{x|x3+x2+x＝0.x∈R}．又∁R(A∪B)＝C.A∩B＝{x|2＜x＜4.x∈R}.试求a.b的值． 解析:∵A＝{x|x＜0或x＞2}.B＝{x|x2-ax+b＜0.x∈R}＝{x|x1＜x＜x2.x1.x2∈R}.C＝{x|x＝0}.∁R(A∪B)＝C＝{0}. ∴A∪B＝{x|x≠0且x∈R}． 又A∩B＝{x|2＜x＜4.x∈R}.可得x1＝0.x2＝4. 又x1.x2是方程x2-ax+b＝0的两根. ∴x1+x2＝a.x1x2＝b. 从而求得a＝4.b＝0.

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