cho a,b,c>0. chứng minh: \(\frac{a^8+b^8+c^8}{a^3+b^3+c^3}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
cho a,b ,c deu duong .cmr
\(\frac{8}{\left(a+b\right)^2+4abc}+\frac{8}{\left(b+c\right)^2+4abc}+\frac{8}{\left(a+c\right)^2+4abc}+a^2+b^2+c^2\ge\frac{8}{a+3}+\frac{8}{b+3}+\frac{8}{c+3}\)
cho số thực a,b,c>0. CMR
\(\frac{8}{\left(a+b\right)^2+4abc}+\frac{8}{\left(b+c\right)^2+4abc}+\frac{8}{\left(c+a\right)^2+4abc}+a^2+b^2+c^2\ge\frac{8}{a+3}+\frac{8}{b+3}+\frac{8}{c+3}\)
cho a,b,c>0. CMR
\(\frac{a^8}{b^3}+\frac{b^8}{c^3}+\frac{c^8}{a^3}\ge a^5+b^5+c^5\)
cho a,b,c là các soos dương thỏa mãn 4(a+b+c)=3abc.
CMR \(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}>=\frac{3}{8}\)
Cho a,b,c dương thỏa: ab+bc+ca
Tìm min \(\frac{a^2}{\sqrt{a^3+8}}+\frac{b^2}{\sqrt{b^3+8}}+\frac{c^2}{\sqrt{c^3+8}}\\ \)
cho a b c la số dương, biết a+b+c<=3. Tìm Pmin
\(P=\frac{a^2}{\left[\sqrt{b^3+8}-\left(c-1\right)^2\right]}+\frac{b^2}{\left[\sqrt{c^3+8}-\left(a-1\right)^2\right]}+\frac{c^2}{\left[\sqrt{a^3+8}-\left(b-1\right)^2\right]}\)
Tìm min,max của P=xyz biết A= \(\frac{8-x^2}{16+x^4}+\frac{8-y^2}{16+y^4}+\frac{8-z^2}{16+z^4}\ge0.\)
Cho a;b;c >0 thỏa mã \(a+b+c\le3\)Tìm min P \(=\left(3+\frac{1}{a}+\frac{1}{b}\right)\left(3+\frac{1}{b}+\frac{1}{c}\right)\left(3+\frac{1}{c}+\frac{1}{a}\right)\)
cho a,b,c>0 CMR:\(\frac{a^8+b^8+c^8}{\left(abc\right)^3}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
