Question

[sweet]

Tìm x,y

a . (x+ 4/ 2007)+ (x+3/2008)=(x+2/2009)+(x+1/2010)

b . 2^x+1 . 3^y-2 = 12^x

Answer 1

[Trần Duy Vương]

a) Theo đề bài, ta có:

\(\dfrac{x+4}{2007}+\dfrac{x+3}{2008}=\dfrac{x+2}{2009}+\dfrac{x+1}{2010}\)

\(\Leftrightarrow\left(\dfrac{x+4}{2007}+1\right)+\left(\dfrac{x+3}{2008}+1\right)=\left(\dfrac{x+2}{2009}+1\right)+\left(\dfrac{x+1}{2010}+1\right)\)

\(\Leftrightarrow\left(\dfrac{x+2011}{2007}+\dfrac{x+2011}{2008}\right)-\left(\dfrac{x+2011}{2009}+\dfrac{x+2011}{2010}\right)=0\)

\(\Leftrightarrow\left(x+2011\right)\left(\dfrac{1}{2007}+\dfrac{1}{2008}-\dfrac{1}{2009}+\dfrac{1}{2010}\right)=0\)

\(\Leftrightarrow x+2011=0\)

\(\) Vậy \(x=-2011\)