chuyển vế + quy đồng + rút gọn ta được: \(\frac{-\left(2a+b\right)^2}{ab\left(2a-b\right)}\ge0\) luôn đúng với mọi a>0>b
Dấu "=" xảy ra khi \(2a=-b\)
cho cho a>0 b<0 cmr \(\frac{1}{a}\ge\frac{2}{b}+\frac{8}{2a-b}\)
Cho a>0, b<0 thỏa mãn a+b>=0. CMR: \(\frac{1}{a}\ge\frac{2}{b}+\frac{8}{2a-b}\)
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: \(\frac{b^2a}{a^3\left(b+c\right)}+\frac{c^2a}{b^3\left(c+a\right)}+\frac{a^2b}{c^3\left(a+b\right)}\ge\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
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: \(\frac{1}{\sqrt{2a+b+1}}+\frac{1}{\sqrt{2b+c+1}}+\frac{1}{\sqrt{2c+a+1}}\ge\frac{3}{2}\)
\(a,b>0\\ a+b=ab\\ CMR:\frac{1}{a^2+2a}+\frac{1}{b^2+2b}+\sqrt{\left(1+a^2\right)\left(1+b^2\right)}\ge\frac{21}{4}\)
Bài toán : Cho a,b > 0
CMR : \(\frac{a^2b}{2a^3+b^3}+\frac{2}{3}\ge\frac{a^2+2ab}{2a^2+b^2}\)
Cho a,b,c>0 và abc=1. CMR:
\(\frac{1}{a^3\left(b+c\right)}+\frac{1}{b^3\left(a+c\right)}+\frac{1}{c^3\left(a+b\right)}\ge\frac{1}{2a}+\frac{1}{2b}+\frac{1}{2c}\)
