已知a>0,b>0,c>0且a+b+c=1,求证a/1+b/1+c/1≥9
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/17 12:44:19
![已知a>0,b>0,c>0且a+b+c=1,求证a/1+b/1+c/1≥9](/uploads/image/z/656786-2-6.jpg?t=%E5%B7%B2%E7%9F%A5a%3E0%2Cb%3E0%2Cc%3E0%E4%B8%94a%2Bb%2Bc%3D1%2C%E6%B1%82%E8%AF%81a%2F1%2Bb%2F1%2Bc%2F1%E2%89%A59)
xP;
B1NBW I^@;{{W6zw73Hݙa};P,b.
6ѣWݒ
"y=Lv~f *4]?*1n,V5Z0KR7K/lHgpf\SR7|-]f!2{
已知a>0,b>0,c>0且a+b+c=1,求证a/1+b/1+c/1≥9
已知a>0,b>0,c>0且a+b+c=1,求证a/1+b/1+c/1≥9
已知a>0,b>0,c>0且a+b+c=1,求证a/1+b/1+c/1≥9
已知a>0,b>0,c>0,a+b+c=1,求证1/a+1/b+1/c≥9
(a+b+c)(1/a+1/b+1/c)
=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c
=1+(b+c)/a+1+(a+c)/b+1+(a+b)/c
=3+(a/b+b/a)+(a/c+c/a)+(b/c+c/b)
≥3+2+2+2=9
1/a+1/b+1/c≥9