Giải phương trình : $(x+2009^{2009})^{2009}+x=2009$
$(x+2009^{2009})^{2009}+x=2009$
Started By Strygwyr, 24-03-2013 - 10:59
#1
Posted 24-03-2013 - 10:59
"Nothing is impossible"
(Napoleon Bonaparte)
#2
Posted 24-03-2013 - 12:13
Giải phương trình : $(x+2009^{2009})^{2009}+x=2009$
Đặt $x+2009^{2009}=a\Rightarrow \left\{\begin{matrix} a^{2009}+x=2009\\ a-x=2009^{2009} \end{matrix}\right.\Rightarrow a^{2009}+a-2009^{2009}-2009=0$
Xét $a > 2009$ thì $ VT > 0$
Xét $ a<2009$ thì $VT <0 $
Xét $ a=2009$ thì VT=0 nên $ x= 2009 - 2009^{2009}$
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