b) Ta có:[tex]\left\{\begin{matrix} \frac{1}{1+a^4}+\frac{1}{1+b^4}\geq \frac{2}{1+a^2b^2}\\ \frac{1}{1+b^4}+\frac{1}{1+c^4}\geq \frac{2}{1+b^2c^2}\\ \frac{1}{1+c^4}+\frac{1}{1+a^4}\geq \frac{2}{1+c^2a^2} \end{matrix}\right.\Rightarrow \frac{1}{1+a^4}+\frac{1}{1+b^4}+\frac{1}{1+c^4}\geq \frac{1}{1+a^2b^2}+\frac{1}{1+b^2c^2}+\frac{1}{1+c^2a^2}[/tex]
Lại có:[tex]\left\{\begin{matrix} \frac{1}{1+a^2b^2}+\frac{1}{1+b^4}\geq \frac{2}{1+ab^3}\\ \frac{1}{1+b^2c^2}+\frac{1}{1+c^4}\geq \frac{2}{1+bc^3}\\ \frac{1}{1+c^2a^2}+\frac{1}{1+a^4}\geq \frac{2}{1+ca^3} \end{matrix}\right.\Rightarrow \frac{1}{1+a^2b^2}+\frac{1}{1+b^4}+\frac{1}{1+b^2c^2}+\frac{1}{1+c^4}+\frac{1}{1+c^2a^2}+\frac{1}{1+a^4}\geq \frac{2}{1+ab^3}+\frac{2}{1+bc^3}+\frac{2}{1+ca^3}\Rightarrow \frac{2}{1+a^4}+\frac{2}{1+b^4}+\frac{2}{1+c^4}\geq \frac{1}{1+a^2b^2}+\frac{1}{1+b^4}+\frac{1}{1+b^2c^2}+\frac{1}{1+c^4}+\frac{1}{1+c^2a^2}+\frac{1}{1+a^4}\geq \frac{2}{1+ab^3}+\frac{2}{1+bc^3}+\frac{2}{1+ca^3}\Rightarrow \frac{1}{1+a^{4}}+\frac{1}{1+b^{4}}+\frac{1}{1+c^{4}}\geq \frac{1}{1+ab^{3}}+\frac{1}{1+bc^{3}}+\frac{1}{1+ca^{3}}[/tex]