Toán Lớp 9: giải phương trình x+1/2008+x+2/2007=x+3/2006+x+4/2005
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Toán Lớp 9: giải phương trình x+1/2008+x+2/2007=x+3/2006+x+4/2005
Comments ( 2 )
\frac{x+1}{2008}+\frac{x+2}{2007}=\frac{x+3}{2006}+\frac{x+4}{2005}
⇔\frac{x+1}{2008}+1+\frac{x+2}{2007}+1=\frac{x+3}{2006}+1+\frac{x+4}{2005}+1
⇔\frac{x+2009}{2008}+\frac{x+2009}{2007}=\frac{x+2009}{2006}+\frac{x+2009}{2005}
⇔(x+2009)(1/2008+1/2009-1/2006-1/2005)=0
Do 1/2008+1/2009-1/2006-1/2005 \ne 0 nên x+2009=0
⇔x=-2009
Vậy x=-2009
Lời giải và giải thích chi tiết:
\frac{x+1}{2008}+\frac{x+2}{2007}=\frac{x+3}{2006}+\frac{x+4}{2005}
<=> (1+\frac{x+1}{2008})+(1+\frac{x+2}{2007})=(1+\frac{x+3}{2006})+(1+\frac{x+4}{2005})
<=> \frac{x+2009}{2008}+\frac{x+2009}{2007}=\frac{x+2009}{2006}+\frac{x+2009}{2005}
<=> \frac{x+2009}{2008}+\frac{x+2009}{2007}-\frac{x+2009}{2006}-\frac{x+2009}{2005}=0
<=> (x+2009)(\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2006}-\frac{1}{2005})=0
mà \frac{1}{2008}+\frac{1}{2007}-\frac{1}{2006}-\frac{1}{2005}≠0
=> x+2009=0
Vậy x=-2009
@Deawoo