2017届高三数学一轮复习第十四篇不等式选讲第2节证明不等式的基本方法基础对点练理.doc

1 2 1 3 2 4 1. ab0, : . : - = = = , ab0, a-b0,ab0,a 2 +b 2 0,a+b0. - 0, . ab0, a+b0, a-b0. = = = =1+ 1. . 2 2. x 1,y 1, x+y+ +xy. : x 1,y 1, x+y+ +xy, xy(x+y)+1 y+x+(xy) 2 . y+x+(xy) 2 -xy(x+y)+1 =(xy) 2 -1-xy(x+y)-(x+y) =(xy+1)(xy-1)-(x+y)(xy-1) =(xy-1)(xy-x-y+1) =(xy-1)(x-1)(y-1), x 1,y 1, (xy-1)(x-1)(y-1) 0, . 3.(2015 ) a0,b0, a+b=+. : (1)a+b 2; (2)a 2 +a0,b0, ab=1. (1) ab=1, a+b 2 =2, a+b 2. (2) a 2 +a0 00,b0,c0, : + + . : + + , +1+ +1+ +1 , + + , 3 (a+b+c) ( + + ) . (a+b+c) ( + + ) = (b+c)+(a+c)+(a+b) ( + + ) 3 3 =, a=b=c = , .