Edited by ongtrum, 29-05-2008 - 01:11.
hay
Started By ongtrum, 29-05-2008 - 01:11
#1
Posted 29-05-2008 - 01:11
ongtrum
-
- Thành viên
-
- 9 posts
Lính mới
cho x,y>0,$x^{y}+y=y^{x}+x.CMR: x+y\leq 1+xy$
#2
Posted 29-05-2008 - 10:07
quangghePT1
-
- Thành viên
-
- 80 posts
Hạ sĩ
$x^{y}-x=y^{x}-y$
*Nếu x>1;y<1 $\rightarrow x^{y}-x<0<y^{x}-y$
*Nếu x<1;y>1$\rightarrow x^{y}-x>0>y^{x}-y$
nên $ (x-1)(y-1)\geq 0\rightarrow x+y\leq 1+xy$
*Nếu x>1;y<1 $\rightarrow x^{y}-x<0<y^{x}-y$
*Nếu x<1;y>1$\rightarrow x^{y}-x>0>y^{x}-y$
nên $ (x-1)(y-1)\geq 0\rightarrow x+y\leq 1+xy$
Edited by quangghePT1, 29-05-2008 - 10:08.
1 user(s) are reading this topic
0 members, 1 guests, 0 anonymous users
