CMR:
$$\frac{a^4+b^4+c^4+a+b+c}{2}\ge \frac{a}{\sqrt{c}}+\frac{b}{\sqrt{a}}+\frac{c}{\sqrt{b}}$$
Edited by E. Galois, 03-01-2013 - 22:01.
-Theo $AM-GM:$Cho $a,b,c>0$ và $abc=1$.
CMR:
$$\frac{a^4+b^4+c^4+a+b+c}{2}\ge \frac{a}{\sqrt{c}}+\frac{b}{\sqrt{a}}+\frac{c}{\sqrt{b}}$$
Có trục trặc gì rồi anh ơi.Nếu áp dụng như vậy thì-Theo $AM-GM:$
$$\dfrac{a^3}{bc}+b\ge 2\dfrac{a}{\sqrt{c}}$$
Xây dựng các BĐT tương tự rồi cộng lại có ĐPCM (Chú ý $abc=1$). Dấu bằng khi $a=b=c=1\ \square$
"If I feel unhappy,I do mathematics to become happy.
If I feel happy,I do mathematics to keep happy."
Alfréd Rényi
Edited by Oral1020, 04-01-2013 - 10:55.
"If I feel unhappy,I do mathematics to become happy.
If I feel happy,I do mathematics to keep happy."
Alfréd Rényi
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