Có 12*(\frac{1}{a
2}+\frac{1}{b
2}+\frac{1}{c
2})=4*(1+1+1)*(
\frac{1}{a2}+\frac{1}{b2}+\frac{1}{c2})\geq4*(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})2 (Bdt B.C.S)\Rightarrow 4*(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})2 \leq 3+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}
\Rightarrow \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq 1 (*)
Có (\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})(a+a+a+a+b+c)\geq62 (Bdt B.C.S)
\Rightarrow (\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq \frac{62}{4a+b+c} (1)
cmtt: (\frac{1}{b}+\frac{1}{b}+\frac{1}{b}+\frac{1}{b}+\frac{1}{c}+\frac{1}{a})\geq\frac{62}{4b+c+a} (2)
(\frac{1}{c}+\frac{1}{c}+\frac{1}{c}+\frac{1}{c}+\frac{1}{a}+\frac{1}{b})\geq\frac{62}{4c+a+b} (3)
Từ (*)(1)(2)(3) \Rightarrow 6\geq \frac{62}{4a+b+c}+\frac{62}{4b+c+a}+\frac{62}{4c+a+b}
\Rightarrow dpcm