cho a,b,c la cac so thuc duong. chung minh rang 2a/(b+c)+2b/(c+a)+2c/(a+b)>=((a-b)^2+(b-c)^2+(c-a)^2)/(a+b+c)^2
Cho a,b.c la cac so duong va abc = 1
Chung minh rang \(\frac{1}{a^2+2b^2+3}+\frac{1}{b^2+2c^2+3}+\frac{1}{c^2+2a^2+3}\le\frac{1}{2}\)
Cho a,b,c\(\ge0\)thoa man abc=1.Chung minh rang
\(\frac{1}{2a^3+3a+2}+\frac{1}{2b^3+3b+2}+\frac{1}{2c^3+3c+2}\)\(\ge\frac{3}{7}\)
Cho a, b,c : abc = 1. Chứng minh:
\(\dfrac{a^2b^2}{2a^2+b^2+3a^2b^2}+\dfrac{b^2c^2}{2b^2+c^2+3b^2c^2}+\dfrac{c^2a^2}{2c^2+a^2+3a^2c^2}\le\dfrac{1}{2}\)
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 \(\frac{bc}{a^2b+a^2c}+\frac{ca}{b^2c+b^2a}+\frac{ab}{c^2a+c^2b}\ge\frac{3}{2}\)
Cho 0<=a,b,c<=1. Chung minh 2(a^3+b^3+c^3)<=3+a^2b+b^2c+c^2a
a,b,c>0: a+b+c=3. Chứng minh:
\(a^2b+b^2c+c^2a>=\frac{9a^2b^2c^2}{1+2a^2b^2c^2}\)
Cho a,b,c là các số dương thỏa mãn a+b+c=3. CMR : a^2b + b^2c + c^2a >= 9a^2b^2c^2/(1+2a^2b^2c^2
cho a, b, c la cac so duong thoa man a\(a^2+b^2+c^2=3\) . Chung minh rang : \(\frac{1}{2-a}+\frac{1}{2-b}+\frac{1}{2-c}>=3\)