Các câu hỏi tương tự
1) cho a;b;c ko âm .chứng minh \(\sqrt{\frac{a+2b}{3}}+\sqrt{\frac{b+2c}{3}}+\sqrt{\frac{c+2a}{3}}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}\)
2) cho a;;b;c dương và abc=1. chứng minh \(\frac{bc}{a^2b+a^2c}+\frac{ca}{b^2c+b^2a}+\frac{ab}{c^2a+c^2b}\ge\frac{3}{2}\)
chứng minh các BĐT 1.frac{a+c}{a+b}+frac{b+d}{b+c}+frac{c+a}{c+d}+frac{b+d}{d+a}ge4với a,b,c,d 02.frac{1}{a}+frac{1}{b}+frac{1}{c}+frac{1}{d}ge4left(frac{1}{2a+b+c}+frac{1}{2b+c+d}+frac{1}{2c+d+a}+frac{1}{2d+a+b}right)3.frac{1}{a^4+b^4+c^4}+frac{2}{a^2b^2+b^2c^2+c^2a^2}geleft(frac{3}{a^2+b^2+c^2}right)^2
với a,b,c04.frac{1}{3x-2}-frac{1}{x-10}+frac{1}{13-2x}gefrac{3}{7}vói x,y t/mfrac{2}{3} x frac{13}{2}
Đọc tiếp
chứng minh các BĐT
1.\(\frac{a+c}{a+b}+\frac{b+d}{b+c}+\frac{c+a}{c+d}+\frac{b+d}{d+a}\ge4\)với a,b,c,d >0
2.\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\ge4\left(\frac{1}{2a+b+c}+\frac{1}{2b+c+d}+\frac{1}{2c+d+a}+\frac{1}{2d+a+b}\right)\)
3.\(\frac{1}{a^4+b^4+c^4}+\frac{2}{a^2b^2+b^2c^2+c^2a^2}\ge\left(\frac{3}{a^2+b^2+c^2}\right)^2\\ \)với a,b,c>0
4.\(\frac{1}{3x-2}-\frac{1}{x-10}+\frac{1}{13-2x}\ge\frac{3}{7}\)vói x,y t/m\(\frac{2}{3}< x< \frac{13}{2}\)
Cho các số thực a, b, c > 0. Chứng minh rằng :
\(\frac{a^2}{\left(2a+b\right)\left(2a+c\right)}+\frac{b^2}{\left(2b+a\right)\left(2b+c\right)}+\frac{c^2}{\left(2c+a\right)\left(2c+b\right)}\ge\frac{1}{3}\)
Câu 1 : Cho a,b,c>0 thỏa mã ab+bc+ac=3. CMR : \(\frac{a}{2a^2+bc}+\frac{b}{2b^2+ac}+\frac{c}{2c^2+ab}\ge abc\)
Câu 2 : Cho a,b,c>0. CMR: \(\frac{2}{a}+\frac{6}{b}+\frac{9}{c}\ge\frac{8}{2a+b}+\frac{48}{3b+2c}+\frac{12}{c+3a}\)
Cho a;b;c >0. CMR:
\(\frac{a^2b}{ab^2+1}+\frac{b^2c}{bc^2+1}+\frac{c^2a}{ca^2+1}\ge\frac{3abc}{1+abc}\)
Cho a,b,c >0 và a+b+c=3
CMR: \(\frac{1}{\sqrt{2a+b+1}}+\frac{1}{\sqrt{2b+c+1}}+\frac{1}{\sqrt{2c+a+1}}\ge\frac{3}{2}\)
Cho a,b,c>0 thỏa mãn \(a+b+c\le3\)
Chứng minh \(\frac{1}{\left(2a+b\right)\left(2c+b\right)}+\frac{1}{\left(2b+c\right)\left(2a+c\right)}+\frac{1}{\left(2c+a\right)\left(2b+a\right)}\ge\frac{3}{\left(a+b+c\right)^2}\)
Cho a,b,c >0 và a2+ b2+c2= 1. Chứng minh :
\(\frac{a^3}{b+2c}+\frac{b^3}{c+2a}+\frac{c^3}{a+2b}\ge\frac{1}{3}\)
Cho a,b,c>0.
Cm:\(\frac{1}{a+3b}+\frac{1}{b+3c}+\frac{1}{c+3a}\ge\frac{1}{2a+b+c}+\frac{1}{a+2b+c}+\frac{1}{a+b+2c}\)