Question

X-10/1999+x-20/1989=x-50/1959+x-80/1929

Giải pt

Cám ơn nhiều

Answer 1

\(\frac{x-10}{1999}+\frac{x-20}{1989}=\frac{x-50}{1959}+\frac{x-80}{1929}\)

\(\Leftrightarrow\frac{x-10}{1999}-1+\frac{x-20}{1989}-1=\frac{x-50}{1959}-1+\frac{x-80}{1929}-1\)

\(\Leftrightarrow\frac{x-2009}{1999}+\frac{x-2009}{1989}-\frac{x-2009}{1959}-\frac{x-2009}{1929}=0\)

\(\Leftrightarrow\left(x-2009\right)\left(\frac{1}{1999}+\frac{1}{1989}-\frac{1}{1959}-\frac{1}{1929}\right)=0\)

Vì \(\frac{1}{1999}+\frac{1}{1989}-\frac{1}{1959}-\frac{1}{1929}\ne0\)

=> x - 2009 = 0

=>   x          = 2009