已知a,b,c.属于R+,( a/b+b/c+c/a)(b/a+c/b+/a/c)≥9求证：已知a,b,c.属于R+,( a/b+b/c+c/a)(b/a+c/b+a/c)≥9

分类: 作业答案 • 2023-01-23 09:29:36

问题描述：

已知a,b,c.属于R+,( a/b+b/c+c/a)(b/a+c/b+/a/c)≥9
求证：已知a,b,c.属于R+,( a/b+b/c+c/a)(b/a+c/b+a/c)≥9

答

(a/b+b/c+c/a)(b/a+c/b+a/c)
=3+(bc/aa+aa/bc)+(bb/ac+ac/bb)+(ab/cc+cc/ab)>=3+2+2+2=9