Question

\(\dfrac{2}{1^2}\cdot\dfrac{6}{2^2}\)\(\cdot\dfrac{12}{3^2}\cdot\dfrac{20}{4^2}\cdot\cdot\cdot\cdot\dfrac{110}{10^2}\)\(\cdot\left(x-2\right)=-20\left(x+1\right)+60\)

giải phương trình trên

Answer 1

\(\dfrac{1.2}{1.1}.\dfrac{2.3}{2.2}.\dfrac{3.4}{3.3}.\dfrac{4.5}{4.4}...\dfrac{10.11}{10.10}\left(x-2\right)=-20x+40\)

\(\Leftrightarrow\dfrac{2.3.4...11}{1.2.3...10}\left(x-2\right)=-20x+40\)

\(\Leftrightarrow11\left(x-2\right)=-20x+40\)

\(\Leftrightarrow11x-22=-20x+40\)

\(\Leftrightarrow31x=62\)

\(\Rightarrow x=2\)

Answer 2

\(=>\dfrac{2\cdot1}{1\cdot1}\cdot\dfrac{2\cdot3}{2\cdot2}\cdot\dfrac{3\cdot4}{3\cdot3}\cdot......\cdot\dfrac{10\cdot11}{10\cdot10}\cdot\left(x-2\right)=-20\left(x+1\right)+60\)=>11*(x-2)=-20*(x+1)+60

=>11x-22=-20x-20+60

=>31x=62

=>x=2