áp dụng BDT AM-GM
\(=>\dfrac{a^4}{b}+\dfrac{b^4}{c}+\dfrac{c^4}{a}\ge3\sqrt[3]{\dfrac{\left(abc\right)\left(abc\right)^3}{abc}}=3abc\)
\(=>15.\left(\dfrac{a^4}{b}+\dfrac{b^4}{c}+\dfrac{c^4}{a}\right)\ge45abc\left(1\right)\)
tương tự \(=>6\left(\dfrac{b}{a^4}+\dfrac{c}{b^4}+\dfrac{a}{c^4}\right)\ge6.3\sqrt[3]{\dfrac{abc}{abc\left(abc\right)^3}}=6.\dfrac{3}{abc}=\dfrac{18}{abc}\left(2\right)\)
\(=>VT\ge45+18=63\)
\(=>VP:21\left(a^4+b^4+c^4\right)\ge21.3abc=63\)
phép cm tương đương\(=>VT-VP\ge63-63=0\)
\(=>VT\ge VP\left(dpcm\right)\)
dấu"=" xay rra \(< =>a=b=c=1\)
Đúng 2
Bình luận (0)
