[tex]Cho a ,b,c \epsilon \mathbb{R}. CMR a^4+b^4+c^4\geq abc(a+b+c)[/tex]
[tex]a^{4}+a^{4}+b^{4}+c^{4}\geq 4a^{2}bc;b^{4}+b^{4}+a^{4}+c^{4}\geq 4b^{2}ac;c^{4}+c^{4}+a^{4}+b^{4}\geq 4c^{2}ab[/tex]
Cong 3 ve ta co: [tex]4(a^{4}+b^{4}+c^{4})\geq 4a^{2}bc+4b^{2}ac+4c^{2}ab=4abc(a+b+c)[/tex]
=>dpcm