Question

Giải phương trình: \(\dfrac{x+10}{2003}+\dfrac{x+6}{2007}+\dfrac{x+12}{2001}+3=0\)

Answer 1

\(\dfrac{x+10}{2003}+\dfrac{x+6}{2007}+\dfrac{x+12}{2001}+3=0\)

\(\Leftrightarrow\dfrac{x+10}{2003}+1+\dfrac{x+6}{2007}+1+\dfrac{x+12}{2001}+1=0\)

\(\Leftrightarrow\dfrac{x+10+2003}{2003}+\dfrac{x+6+2007}{2007}+\dfrac{x+12+2001}{2001}=0\)

\(\Leftrightarrow\dfrac{x+2013}{2003}+\dfrac{x+2013}{2007}+\dfrac{x+2013}{2001}=0\)

\(\Leftrightarrow\left(x+2003\right)\left(\dfrac{1}{2003}+\dfrac{1}{2007}+\dfrac{1}{2001}\right)=0\)

\(\Leftrightarrow x+2013=0\)

\(\Leftrightarrow x=-2013\)

Vậy pt có nghiệm x = -2013

Answer 2

\(\dfrac{x+10}{2003}\)+\(\dfrac{x+6}{2007}\)+\(\dfrac{x+12}{2001}\)+3=0

<=> \(\dfrac{x+10}{2003}\)+1+\(\dfrac{x+6}{2007}\)+1+\(\dfrac{x+12}{2001}\)+1=0

<=> (\(\dfrac{x+10}{2003}\)+1) + (\(\dfrac{x+6}{2007}\)+1) + (\(\dfrac{x+12}{2001}\)+1)=0

<=> \(\dfrac{x+2013}{2003}\)+\(\dfrac{x+2013}{2007}\)+\(\dfrac{x+2013}{2001}\)=0

<=> (x+2013)(\(\dfrac{1}{2003}+\dfrac{1}{2007}+\dfrac{1}{2001}\))=0

<=> x+2013=0( Vì \(\dfrac{1}{2003}+\dfrac{1}{2007}+\dfrac{1}{2001}\)>0)

<=> x= -2013

Vậy S={-2013}