题目

已知ab≠0,求证：a+b=1的充要条件是a3+b3+ab-a2-b2=0. 答案：证明：必要性：∵a+b=1,即b=1-a,∴a3+b3+ab-a2-b2=a3+（1-a）3+a（1-a）-a2-（1-a）2=a3+1-3a+3a2-a3+a-a2-a2-1+2a-a2=0.充分性：∵a3+b3+ab-a2-b2=0,即（a+b）（a2-ab+b2）-（a2-ab+b2）=0,∴（a2-ab+b2）（a+b-1）=0.由ab≠0,即a≠0且b≠0,∴a2-ab+b2=（a-）2+≠0,只有a+b=1.综上可知，当ab≠0时，a+b=1的充要条件是a3+b3+ab-a2-b2=0.根据提示，写故事。请你根据下面的提示，发挥想象，写出Lucy的周末故事。人物：Lucy, Mary and Tiantian; Lucy's dog天气：sunny and windy时间：last Sunday地点：a supermarket; Renmin Park事件：buy a kite; ride a bike for three people; fly kites心情：laugh, happy, tiredLucy's last weekend____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________