Violympic toán 9
Các câu hỏi tương tự
Bài 1: Cho a,b,c \(\ge\)0. CMR: \(\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c}\ge6\)
Bài 2: Cho a,b,c \(\ge\)0. CMR: \(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge\frac{3}{2}\)
Cho a,b,c>0 CMR \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{a+b}{b+c}+\frac{b+c}{a+b}+1\)
BL
28 tháng 10 2019 lúc 23:28
1. Cho a,b,c>0. Cmr: \(\frac{a}{\left(b+c\right)^2}+\frac{b}{\left(c+a\right)^2}+\frac{c}{\left(a+b\right)^2}\ge\frac{9}{4\left(a+b+c\right)}\)
(4)Bài 1:Với forall ab0. CMR: a+ frac{1}{bleft(a-bright)}ge3
(7) Bài 2: Cho a,b,c ne 0 .CMR: frac{a^2}{b^2}+frac{b^2}{c^2}+frac{c^2}{a^2}gefrac{b}{a}+frac{c}{b}+frac{a}{c}
(8) Bài 3: Cho a,b,c0 thõa mãn abc1
CMR: frac{b+c}{sqrt{a}}+frac{c+a}{sqrt{b}}+frac{a+b}{sqrt{c}}gesqrt{a}+sqrt{b}+sqrt{c}+3
Đọc tiếp
(4)Bài 1:Với \(\forall\) a>b>0. CMR: a+ \(\frac{1}{b\left(a-b\right)}\ge3\)
(7) Bài 2: Cho a,b,c \(\ne\) 0 .CMR: \(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}\ge\frac{b}{a}+\frac{c}{b}+\frac{a}{c}\)
(8) Bài 3: Cho a,b,c>0 thõa mãn abc=1
CMR: \(\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}+3\)
LD
7 tháng 7 2019 lúc 16:55
Cho a,b,c > 0. cmr:
\(\frac{a^2}{b^2+c^2}+\frac{b^2}{c^2+a^2}+\frac{c^2}{a^2+b^2}\ge\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\)
Cho a,b,c > 0 và a+b+c ≤ 1. CMR: A = \(\frac{1}{a^2+2bc}+\frac{1}{b^2+2ca}+\frac{1}{c^2+2ab}\) ≥ 9
Bài 1: Cho \(a,b,c>0;a+b+c=9\). CMR:
\(\frac{a^3+b^3}{ab+9}+\frac{b^3+c^3}{bc+9}+\frac{c^3+a^3}{ca+9}\ge9\)
Bài 2: Cho \(a,b,c>0;a^2+b^2+c^2=3\). CMR:
\(\frac{a^2}{a+b^2}+\frac{b^2}{b+c^2}+\frac{c^2}{c+a^2}\ge\frac{a+b+c}{2}\)
Akai Haruma đây nha chị :D
cho c ≥ b ≥ a > 0
CMR \(\frac{a}{b}\) + \(\frac{b}{c}\) + \(\frac{c}{a}\) ≥ \(\frac{b}{a}\) + \(\frac{c}{b}\) + \(\frac{a}{c}\)
\(\frac{a}{b}\)\(\frac{a}{b}\)
Cho a,b,c \(\ge\)0 .
CMR: \(\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\ge\frac{3\left(a^2+b^2+c^2\right)}{a+b+c}\)