Cho các số thực dương a,b,c.CM
$\frac{2.(a^{3}+b^{3}+c^{3})}{abc}+\frac{9.(a+b+c)^{2}}{a^{2}+b^{2}+c^{2}}\geq 33$
à xin lỗi, hjhj đồ ngu –  jangdaica12 11-05-16 12:00 AM
anh ghi sai đề:v –  ๖ۣۜJinღ๖ۣۜKaido 10-05-16 11:59 PM
ns ai ngốc zậy hả? –  Ngọc 10-05-16 11:59 PM
sai đề kìa, lêu lêu hjhj đồ ngôk –  jangdaica12 10-05-16 11:57 PM
cmnr ghi sai đề... hèn chi ntdp ra –  ๖ۣۜJinღ๖ۣۜKaido 10-05-16 11:55 PM
$\Leftrightarrow \frac{(a^3+b^3+c^3)(a+b+c)}{abc(a+b+c)}+\frac{9(a+b+c)^2}{a^2+b^2+c^2}\geq 30$
$\Rightarrow \frac{9}{2}\frac{(a^2+b^2+c^2)^2}{abc(a+b+c)}+\frac{9(a+b+c)^2}{2(a^2+b^2+c^2)}+\frac{9(a+b+c)^2}{2(a^2+b^2+c^2)}-\frac{7}{2}\frac{(a^2+b^2+c^2)^2}{abc(a+b+c)}\geq 3\sqrt[3]{\frac{9^3(a+b+c)^3}{2^3abc}}-\frac{7}{2}\frac{(a+b+c)^3}{9abc}\geq 30$
hôm nay ca mệt quá, mai ca chữa cho rõ luôn nhé –  ๖ۣۜDevilღ 11-05-16 12:27 AM
bdt đã cho $\Leftrightarrow \frac{2(a^3+b^3+c^3)}{abc}+\frac{9(a^2+b^2+c^2)+18(ab+bc+ca)}{a^2+b^2+c^2} \ge 33$
$\Leftrightarrow \frac{a^3+b^3+c^3}{abc}+\frac{9(ab+bc+ca)}{a^2+b^2+c^2} \ge 12$
$\Leftrightarrow \frac{a^3+b^3+c^3-3abc}{abc}+\frac{9(ab+bc+ca-a^2-b^2-c^2)}{a^2+b^2+c^2} \ge0$
$\Leftrightarrow \frac{(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}{abc} \ge\frac{9(a^2+b^2+c^2-ab-bc-ca)}{a^2+b^2+c^2}$
$\Leftrightarrow \frac{a+b+c}{abc} \ge\frac{9}{a^2+b^2+c^2}$ (chia 2 vế cho $\sum a^2-\sum ab \ge0$)
$\Leftrightarrow (a+b+c)(a^2+b^2+c^2) \ge9abc$ 
BDT cuối hiển nhiên đúng theo $AM-GM$ :
 $(a+b+c)(a^2+b^2+c^2) \ge 3\sqrt[3]{abc}.3\sqrt[3]{a^2b^2c^2}=9abc$
~~~~
BDT đc cm, dấu bằng xảy ra $\Leftrightarrow a=b=c=1$

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