当代印度著名诗人泰戈尔在《世界上最遥远的距离》中写道,世界上最遥远的距离,不是瞬间便无处寻觅,而是尚未相遇,便注定无法相聚。距离是数学、天文学、物理学中的热门话题,唯有对宇宙距离进行测量,人类才能掌握世界尺度. 我们可以从图形和代数化简两个角度来计算距离:
①已知点A,B在数轴上分别表示有理数a,b,A,B两点之间的距离表示为AB=|a-b|,例如|x-2|表示x到2的距离,而|a+1|=|a-(-1)|则表示a到-1的距离;
②我们知道:
于是可以用这一结论来化简含有绝对值的代数式.
例如化简|x+1|+|x-2|时,可先令x+1=0和x-2=0,分别求得x=-1,x=2(称-1和2分别为|x+1|+|x-2|的零点值) ,在实数范围内,零点值x=-1和x=2可将全体实数分成不重复且不遗漏的如下 3种情况:
①x<-1; ②-1≤x<2; ③x≥2. 从而化简|x+1|+|x-2|可分以下3种情况:
①当x<-1时,原式=-(x+1)-(x-2)=-2x+1;
②当-1≤x<2时,原式=x+1-(x-2)=3;
③当x≥2时,原式=x+1+x-2=2x-1.
综上,原式 ![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%22%3E%3Cmrow%3E%3Cmtable%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmfenced%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
结合以上材料,回答以下问题: