Question

Cho a,b,c>0.CMR:

\(\frac{1}{a^4}+\frac{1}{b^4}+\frac{1}{c^4}\ge\frac{2a}{a^6+b^4}+\frac{2b}{b^6+c^4}+\frac{2c}{c^6+a^4}\)

Answer 1

Ta có:

\(VT\ge\frac{1}{a^2b^2}+\frac{1}{b^2c^2}+\frac{1}{c^2a^2}=\frac{a}{a^3.b^2}+\frac{b}{b^3.c^2}+\frac{c}{c^3.a^2}\)

\(VT\ge\frac{a}{\frac{\left(a^3\right)^2+\left(b^2\right)^2}{2}}+\frac{b}{\frac{\left(b^3\right)^2+\left(c^2\right)^2}{2}}+\frac{c}{\frac{\left(c^3\right)^2+\left(a^2\right)^2}{2}}=VP\)

Dấu "=" xảy ra khi \(a=b=c=1\)