Cho a,b,c>0 thỏa mãn a.b.c=1. Tìm GTNN của \(T=\frac{a^5}{b^3+c^2}+\frac{b^5}{c^3+a^2}+\frac{c^5}{a^3+b^2}+\frac{1}{4}\left(a^4+b^4+c^4\right)\)
cho a,b,c > 0 thỏa mãn a+b+c = 3. Cmr:
\(\frac{a^3}{b^2+c^2}+\frac{b^3}{c^2+a^2}+\frac{c^3}{a^2+b^2}\ge\frac{3}{2}\)
cho a,b,c > 0 . Cmr:
\(\frac{a^3}{a^2+ab+b^2}+\frac{b^3}{b^2+bc+c^2}+\frac{c^3}{c^2+ca+a^2}\ge\frac{a+b+c}{3}\)
CHo a,b,c,d>0 thỏa mãn abcd=1. CMR \(\frac{a^3}{b^2(c^2+d^2)}+\frac{b^3}{c^2(d^2+a^2)} +\frac{c^3}{d^2(a^2+b^2)}+\frac{d^3}{a^2(b^2+c^2)} \geq 2\)
cho a,b,c > 0,a+b+c=3
tìm GTNN của P=\(\frac{a}{1+b^2}\)+\(\frac{b}{1+c^2}\)+\(\frac{c}{1+a^2}\)
CMR \(\frac{a^3}{a^2+b^2}+\frac{b^3}{b^2+c^2}+\frac{c^3}{c^2+a^2}>=\frac{a+b+c}{2}\) với a,b,c >0
cho a,b,c>0 cm
\(\frac{a^3}{b^2}+\frac{b^3}{c^2}+\frac{c^3}{a^2}\ge a+b+c\)
cho a,b,c> 0 thỏa mãn ab+bc+ca =3. Cmr:
\(\frac{a^3}{b^2+3}+\frac{b^3}{c^2+3}+\frac{c^3}{a^2+3}\ge\frac{3}{4}\)
cho a,b,c >0 và a+b+c=3 . cmr :
\(\frac{a}{\sqrt{b+c+2}}+\frac{b}{\sqrt{a+c+2}}+\frac{c}{\sqrt{a+b+2}}\ge\frac{3}{5}\)
