Question

8．如果|x-y|=y-x，且x²=4，|y|=3，則x+y=5或1．

Answer 1

分析 先根據(jù)平方根和絕對(duì)值，確定x，y的值，再根據(jù)|x-y|=y-x，進(jìn)一步得到$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$或$\left\{\begin{array}{l}{x=-2}\\{y=3}\end{array}\right.$，即可解答．

解答 解：∵x²=4，|y|=3，
∴x=2或-2，y=3或-3，
∵|x-y|=y-x，
∴$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$或$\left\{\begin{array}{l}{x=-2}\\{y=3}\end{array}\right.$
∴x+y=5或1，
故答案為：5或1．

點(diǎn)評(píng) 本題考查了絕對(duì)值，解決本題的關(guān)鍵是熟記絕對(duì)值的性質(zhì)．