Question

Giải phương trình sau:

\(\frac{x-241}{17}\) + \(\frac{x-220}{19}\) + \(\frac{x-195}{21}\) + \(\frac{x-166}{23}\) = 10

Answer 1

\(\frac{x-241}{17}+\frac{x-220}{19}+\frac{x-195}{21}+\frac{x-166}{23}=10\)

\(\Leftrightarrow\)   \(\frac{x-241}{17}+\frac{x-220}{19}+\frac{x-195}{21}+\frac{x-166}{23}-10=0\)

\(\Leftrightarrow\)  \(\left(\frac{x-241}{17}-1\right)+\left(\frac{x-220}{19}-2\right)+\left(\frac{x-195}{21}-3\right)+\left(\frac{x-166}{23}-4\right)=0\)

\(\Leftrightarrow\)   \(\frac{x-258}{17}+\frac{x-258}{19}+\frac{x-258}{21}+\frac{x-166}{23}=0\)

\(\Leftrightarrow\)   \(\left(x-258\right)\left(\frac{1}{17}+\frac{1}{19}+\frac{1}{21}+\frac{1}{21}\right)=0\)

\(\Leftrightarrow\)   \(x-258=0\)  \(\Leftrightarrow\)  \(x=258\)