Question

Giải phương trình \(\dfrac{x+1}{39}+\dfrac{x+2}{38}+\dfrac{x+3}{37}=0\)

Mong mọi ng giúp đỡ

Answer 1

\(\dfrac{x+1}{39}+\dfrac{x+2}{38}+\dfrac{x+3}{37}=0\)

\(\Leftrightarrow\dfrac{x+1}{39}+1+\dfrac{x+2}{38}+1+\dfrac{x+3}{37}+1-3=0\)

\(\Leftrightarrow\dfrac{x+40}{39}+\dfrac{x+40}{38}+\dfrac{x+40}{37}=3\)

\(\Leftrightarrow\left(x+40\right)\left(\dfrac{1}{39}+\dfrac{1}{38}+\dfrac{1}{37}\right)=3\)

\(\Leftrightarrow\left(x+40\right).\dfrac{4331}{54834}=3\)

\(\Leftrightarrow x+40=\dfrac{164502}{4331}\)

\(\Leftrightarrow x=\dfrac{-8738}{4331}\)

-Vậy \(S=\left\{\dfrac{-8738}{4331}\right\}\)