Câu 1: Giải phương trình sau
(x-1009)/1001 + (x-4)/1003 + (x+2010)/1005 =7
Câu 2: Giải phương trình sau
(x-3)/2011 + (x-2)/2012 = (x-2012)/2 + (x-2011)/3
Câu 1: Giải phương trình sau
(x-1009)/1001 + (x-4)/1003 + (x+2010)/1005 =7
Câu 2: Giải phương trình sau
(x-3)/2011 + (x-2)/2012 = (x-2012)/2 + (x-2011)/3
Đáp án: Câu 1: $x=2010$ Câu 2: $x=2014$
Giải thích các bước giải:
Câu 1:
$\dfrac{x-1009}{1001}+\dfrac{x-4}{1003}+\dfrac{x+2010}{1005}=7$
$\to( \dfrac{x-1009}{1001}-1)+(\dfrac{x-4}{1003}-2)+(\dfrac{x+2010}{1005}-4)=0$
$\to\dfrac{x-1009-1001}{1001}+\dfrac{x-4-2\cdot1003}{1003}+\dfrac{x+2010-4\cdot1005}{1005}=0$
$\to\dfrac{x-2010}{1001}+\dfrac{x-2010}{1003}+\dfrac{x-2010}{1005}=0$
$\to(x-2010)(\dfrac{1}{1001}+\dfrac{1}{1003}+\dfrac{1}{1005})=0$
$\to x-2010=0$
$\to x=2010$
Câu 2:
$\dfrac{x-3}{2011}+\dfrac{x-2}{2012}=\dfrac{x-2012}{2}+\dfrac{x-2011}{3}$
$\to (\dfrac{x-3}{2011}-1)+(\dfrac{x-2}{2012}-1)=(\dfrac{x-2012}{2}-1)+(\dfrac{x-2011}{3}-1)$
$\to \dfrac{x-3-2011}{2011}+\dfrac{x-2-2012}{2012}=\dfrac{x-2012-2}{2}+\dfrac{x-2011-3}{3}$
$\to \dfrac{x-2014}{2011}+\dfrac{x-2014}{2012}=\dfrac{x-2014}{2}+\dfrac{x-2014}{3}$
$\to \dfrac{x-2014}{2011}+\dfrac{x-2014}{2012}-\dfrac{x-2014}{2}-\dfrac{x-2014}{3}=0$
$\to (x-2014)(\dfrac{1}{2011}+\dfrac{1}{2012}-\dfrac{1}{2}-\dfrac{1}{3})=0$
$\to x-2014=0$
$\to x=2014$