Các câu hỏi tương tự
1) Cho a,b,c,d>0. cmr:
a)\(\frac{a}{b}+\frac{b}{c}+\frac{c}{d}>=\frac{a+b+c}{\sqrt[3]{abc}}\)
b)\(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{d^2}+\frac{d^2}{e^2}>=\frac{a+b+c+d}{\sqrt[4]{abcd}}\)
B5:
a,c,b,d>0
CMR: \(\frac{a}{b+c}+\frac{b}{c+d}+\frac{c}{d+a}+\frac{d}{a+b}>=2\)
B6;
a,b,c>0
CMR: \(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}>=\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\)
b) \(2< \frac{\left(a+b\right)}{a+b+c}+\frac{\left(b+c\right)}{b+c+d}+\frac{\left(c+d\right)}{c+d+a}+\frac{\left(d+a\right)}{d+a+b}< 4\)
Cho a,b,c,d > 0 CMR :
a)\(A=\frac{\left(a+c\right)}{a+b}+\frac{\left(b+d\right)}{b+c}+\frac{\left(c+a\right)}{c+d}+\frac{\left(d+b\right)}{d+a}4\ge\)
Cho a, b, c, d >0. CMR:
\(\frac{a}{b+c}+\frac{b}{c+d}+\frac{c}{d+a}+\frac{d}{a+b}\ge2\)
Cho a,b,c,d>0 thỏa abcd=1. CMR \(\frac{a^3}{b^2\left(c^2+d^2\right)}+\frac{b^3}{c^2\left(d^2+a^2\right)}+\frac{c^3}{d^2\left(a^2+b^2\right)}+\frac{d^3}{a^2\left(b^2+c^2\right)}\ge2\)
Bài 1:Cho a,b,c,d là các số dương. Chứng minh rằng :frac{a^4}{left(a+bright)left(a^2+b^2right)}+frac{b^4}{left(b+cright)left(b^2+c^2right)}+frac{c^4}{left(c+dright)left(c^2+d^2right)}+frac{d^4}{left(d+aright)left(d^2+a^2right)}gefrac{a+b+c+d}{4}Bài 2:Cho a0,b0,c0.CM:frac{a}{bc}+frac{b}{ca}+frac{c}{ab}ge2left(frac{1}{a}+frac{1}{b}+frac{1}{c}right)Bài 3: a) Cho x,y,0. CMR:frac{x^3}{x^2+xy+y^2}gefrac{2x-y}{3}b) Chứng minh rằngSigmafrac{a^3}{a^2+ab+b^2}gefrac{a+b+c}{3}
Đọc tiếp
Bài 1:Cho a,b,c,d là các số dương. Chứng minh rằng :
\(\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+d\right)\left(c^2+d^2\right)}+\frac{d^4}{\left(d+a\right)\left(d^2+a^2\right)}\ge\frac{a+b+c+d}{4}\)
Bài 2:Cho \(a>0,b>0,c>0\).\(CM:\frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab}\ge2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
Bài 3: a) Cho x,y,>0. CMR:\(\frac{x^3}{x^2+xy+y^2}\ge\frac{2x-y}{3}\)
b) Chứng minh rằng\(\Sigma\frac{a^3}{a^2+ab+b^2}\ge\frac{a+b+c}{3}\)
cho a, b, c, d >0
tim GTNN :
S=\(\frac{a}{b+c+d}+\frac{b}{a+c+d}+\frac{c}{a+b+d}+\frac{d}{a+b+c}+\frac{b+c+d}{a}+\frac{a+c+d}{b}+\frac{a+b+d}{c}+\frac{a+b+c}{d}\)
Cho a,b,c,d là 4 số thực dương thỏa mãn a+b+c+d=1.CMR:
\(\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+d}+\frac{d^2}{d+a}\ge\frac{1}{2}\)
Bài 1: Cho a,b,c,d dương CMR: 1<\(\frac{a}{a+b+c}+\frac{b}{b+c+d}+\frac{c}{a+c+d}+\frac{d}{a+b+d}\)<2
Bài 2:CMR:Nếu a,b,c là độ dài 3 cạnh của tam giác thì \(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\)<2