Tìm GTNN:$\frac{x^2+2x+3}{(x+2)^2}$
Edited by Mikhail Leptchinski, 26-10-2014 - 22:08.
Tìm GTNN:$\frac{x^2+2x+3}{(x+2)^2}$
Started By Chung Anh, 26-10-2014 - 18:03
#2
Posted 26-10-2014 - 18:14
hoanglong2k
-
- Điều hành viên THCS
-
- 965 posts
Trung úy
ĐK $x\neq -2$
Đặt $A=\frac{x^{2}+2x+3}{(x+2)^{2}}\Rightarrow 3A=\frac{3x^{2}+6x+9}{(x+2)^{2}}=\frac{2x^{2}+8x+8}{x^{2}+4x+4}+\frac{x^{2}-2x+1}{(x+2)^{2}}=2+(\frac{x-1}{x+2})^{2}\geq 2\Rightarrow A\geq \frac{2}{3}$
Vậy GTNN của A là $\frac{2}{3}$ khi x=1
Edited by hoanglong2k, 26-10-2014 - 19:38.
- Chung Anh and Hoang Long Le like this
1 user(s) are reading this topic
0 members, 1 guests, 0 anonymous users
