Question

Mấy chế giúp pu pài này nhớ!^_^

Giải phương trình:

\(\frac{x-5}{1996}+\frac{x-15}{1986}=\frac{x-1986}{15}+\frac{x+1996}{5}\)

Thank mọi người nhju!!^_^

Answer 1

\(\frac{x-5}{1996}-1+\frac{x-15}{1986}-1=\frac{x-1986}{15}-1+\frac{x-1996}{5}-1\)

\(\Leftrightarrow\frac{x-2001}{1996}+\frac{x-2001}{1986}=\frac{x-2001}{15}+\frac{x-2001}{5}\)

\(\Leftrightarrow\frac{x-2001}{1996}+\frac{x-2001}{1986}-\frac{x-2001}{15}-\frac{x-2001}{5}=0\)

\(\Leftrightarrow\left(x-2001\right)\left(\frac{1}{1996}+\frac{1}{1986}-\frac{1}{15}-\frac{1}{5}\right)=0\)

\(\Leftrightarrow x-2001=0\)

\(\Leftrightarrow x=2001\)

\(S=\left\{2001\right\}\)