\(\dfrac{2}{1^2}.\dfrac{6}{2^2}.\dfrac{12}{3^2}.\dfrac{20}{4^2}.....\dfrac{110}{10^2}.x=-20\)
\(\dfrac{1.2}{1^2}.\dfrac{2.3}{2^2}.\dfrac{3.4}{3^2}.\dfrac{4.5}{4^2}.....\dfrac{10.11}{10^2}.x=-20\)
\(\dfrac{1.2.2.3.3.4.4.5.5.....10.10.11}{1.1.2.2.3.3.4.4.5.5.....10.10}.x=-20\)
\(11.x=-20\)
\(x=-20:11=-\dfrac{20}{11}\)
\(\dfrac{2}{1^2}\cdot\dfrac{6}{2^2}\cdot\dfrac{12}{3^2}\cdot\dfrac{20}{4^2}\cdot...\cdot\dfrac{110}{10^2}\cdot x=-20\)
\(\Leftrightarrow\dfrac{1\cdot2}{1\cdot1}\cdot\dfrac{2\cdot3}{2\cdot2}\cdot\dfrac{3\cdot4}{3\cdot3}\cdot\dfrac{4\cdot5}{4\cdot4}\cdot...\cdot\dfrac{10\cdot11}{10\cdot10}\cdot x=-20\)
\(\Leftrightarrow\dfrac{1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot...\cdot10\cdot11}{1\cdot1\cdot2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot10\cdot10}\cdot x=-20\)
\(\Rightarrow11\cdot x=-20\)
\(\Rightarrow x=\dfrac{-20}{11}\)
Vậy \(x=\dfrac{-20}{11}\).
