Question

[Thái Hoàng]

Giúp mình bài 3, 4 gấp. Mình sắp thi rồi. Pl/s

Answer 1

[Nguyễn Hoàng Minh]

Bài 4:

\(\left\{{}\begin{matrix}a^4+b^4\ge2a^2b^2\\b^4+c^4\ge2b^2c^2\\c^4+a^4\ge2a^2c^2\end{matrix}\right.\\ \Leftrightarrow2\left(a^4+b^4+c^4\right)\ge2\left(a^2b^2+b^2c^2+c^2a^2\right)\\ \Leftrightarrow a^4+b^4+c^4\ge a^2b^2+b^2c^2+c^2a^2\left(1\right)\\ \left\{{}\begin{matrix}a^2b^2+b^2c^2\ge2ab^2c\\b^2c^2+c^2a^2\ge2abc^2\\c^2a^2+a^2b^2\ge2a^2bc\end{matrix}\right.\\ \Leftrightarrow2\left(a^2b^2+b^2c^2+c^2a^2\right)\ge2\left(a^2bc+ab^2c+abc^2\right)\\ \Leftrightarrow a^2b^2+b^2c^2+c^2a^2\ge a^2bc+ab^2c+abc^2=abc\left(a+b+c\right)\left(2\right)\\ \left(1\right)\left(2\right)\Leftrightarrow a^4+b^4+c^4\ge abc\left(a+b+c\right)\)

Dấu \("="\Leftrightarrow a=b=c\)