Question

20．已知集合M={1，2，a，a²-3a-1}，N={-1，3}，若N?M，求a的值．

Answer 1

分析 由题意知$\left\{\begin{array}{l}{a=-1}\\{{a}^{2}-3a-1=3}\end{array}\right.$或$\left\{\begin{array}{l}{a=3}\\{{a}^{2}-3a-1=-1}\end{array}\right.$，从而解得．

解答 解：∵N?M，
∴$\left\{\begin{array}{l}{a=-1}\\{{a}^{2}-3a-1=3}\end{array}\right.$或$\left\{\begin{array}{l}{a=3}\\{{a}^{2}-3a-1=-1}\end{array}\right.$，
解得，a=-1或a=3．

点评 本题考查了真子集的应用，属于基础题．