Question

5．已知集合A={3，4，5}，集合B={a²，5，|b|}，且A=B，求a，b的值．

Answer 1

分析 根據相等集合的定義，得到關于a，b的方程組，解出即可．

解答 解：∵A={3，4，5}，B={a²，5，|b|}，A=B，
∴$\left\{\begin{array}{l}{{a}^{2}=3}\\{|b|=4}\end{array}\right.$或$\left\{\begin{array}{l}{{a}^{2}=4}\\{|b|=3}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=\sqrt{3}}\\{b=4}\end{array}\right.$或$\left\{\begin{array}{l}{a=\sqrt{3}}\\{b=-4}\end{array}\right.$或$\left\{\begin{array}{l}{a=-\sqrt{3}}\\{b=4}\end{array}\right.$或$\left\{\begin{array}{l}{a=-\sqrt{3}}\\{b=-4}\end{array}\right.$，
或$\left\{\begin{array}{l}{a=2}\\{b=3}\end{array}\right.$或$\left\{\begin{array}{l}{a=2}\\{b=-3}\end{array}\right.$或$\left\{\begin{array}{l}{a=-2}\\{b=3}\end{array}\right.$或$\left\{\begin{array}{l}{a=-2}\\{b=-3}\end{array}\right.$．

點評 本題考查了相等集合的定義，是一道基礎題．