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Cho a,b,c>0.CMR: \(\frac{1}{2a+b}+\frac{1}{2b+c}+\frac{1}{2c+a}\ge\frac{3}{a+b+c}\)
a) cho x,y,z>0 sao cho xyz=1. CMR \(\frac{x^4y}{x^2+1}+\frac{y^4z}{^{y^2+1}}+\frac{z^4x}{^{z^2+1}}\ge\frac{3}{2}\)
b) cho a,b,c,d>0 sao cho a+b+c+d=4. CMR \(\frac{a}{1+b^2c}+\frac{b}{1+c^2d}+\frac{c}{1+d^2a}+\frac{d}{1+a^2d}\ge2\)
CMR\(a^4+b^4\ge\frac{1}{8}\)biết a+b=1 và a,b>0
cho a,b,c lớn lơn 0 CMR :\(\frac{a^3}{a+2b}\)+\(\frac{b^3}{b+2c}\)+\(\frac{c^3}{c+2a}\)\(\ge\frac{a^2+b^2+c^2}{3}\)
Cho a,b,c>0 và abc=1
CMR\(\frac{a}{ab+1}+\frac{b}{bc+1}+\frac{c}{ca+1}\ge\frac{3}{2}\)
cho a,b,c,d > 0. CMR \(\frac{a^4}{a^3+2b^3}+\frac{b^4}{b^3+2c^3}+\frac{c^4}{c^3+2d^3}+\frac{d^4}{d^3+2a^3}\ge\frac{a+b+c+d}{3}\)
cho a;b;c >0 và \(a^2+b^2+c^2=1\)
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:\(\frac{a^2b}{2a^3+b^3}+\frac{2}{3}\ge\frac{a^2+2ab}{2a^2+b^2}\)
Cho a, b, c, d > 0. CMR \(\frac{a^4}{a^3+2b^3}+\frac{b^4}{a^3+2b^3}+\frac{c^4}{c^3+2d^3}+\frac{d^4}{d^3+2a^3}\ge\frac{a+b+c+d}{3}\)