Question

Answer 1

ĐKXĐ: \(x\ge0\)

\(\left|x+\dfrac{1}{6}\right|+\left|x+\dfrac{1}{12}\right|+...+\left|x+\dfrac{1}{110}\right|=12x\)

\(\Rightarrow x+\dfrac{1}{2.3}+x+\dfrac{1}{3.4}+...+x+\dfrac{1}{10.11}=12x\)

\(\Rightarrow9x+\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{10}-\dfrac{1}{11}\right)=12x\)

\(\Rightarrow3x=\dfrac{1}{2}-\dfrac{1}{11}=\dfrac{9}{22}\Rightarrow x=\dfrac{3}{22}\)