Question

Tìm x biết \(\dfrac{x}{6}+\dfrac{x}{10}+\dfrac{x}{15}+\dfrac{x}{21}+\dfrac{x}{28}+\dfrac{x}{36}+\dfrac{x}{45}+\dfrac{x}{55}+\dfrac{x}{66}+\dfrac{x}{78}=\dfrac{220}{39}\)

Answer 1

\(\dfrac{x}{6}+\dfrac{x}{10}+\dfrac{x}{15}+........+\dfrac{x}{78}=\dfrac{220}{39}\)

\(\Leftrightarrow\dfrac{2x}{12}+\dfrac{2x}{20}+........+\dfrac{2x}{156}=\dfrac{220}{39}\)

\(\Leftrightarrow2x\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+..........+\dfrac{1}{12.13}\right)=\dfrac{220}{39}\)

\(\Leftrightarrow2x\left(\dfrac{1}{3}-\dfrac{1}{13}\right)=\dfrac{220}{39}\)

\(\Leftrightarrow2x.\dfrac{10}{39}=\dfrac{220}{39}\)

\(\Leftrightarrow x.\dfrac{20}{39}=\dfrac{220}{39}\)

\(\Leftrightarrow x=11\)

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