Question

X - 10 / 1999 + x - 20/1989 = x - 50/1969 + x - 80/1929. Em xin được mọi người giúp đỡ ạ

Answer 1

\(\dfrac{x-10}{1999}+\dfrac{x-20}{1989}=\dfrac{x-50}{1969}+\dfrac{x-80}{1929}\)

Trừ 2 cho hai vế, thu được: \(\left(\dfrac{x-10}{1999}-1\right)+\left(\dfrac{x-20}{1989}-1\right)=\left(\dfrac{x-50}{1969}-1\right)+\left(\dfrac{x-80}{1929}-1\right)\)

\(\Leftrightarrow\dfrac{x-2009}{1999}+\dfrac{x-2009}{1989}=\dfrac{x-2009}{1969}+\dfrac{x-2009}{1929}\)

\(\Leftrightarrow\left(x-2009\right)\left(\dfrac{1}{1999}+\dfrac{1}{1989}-\dfrac{1}{1969}-\dfrac{1}{1929}\right)=0\)

\(\Rightarrow x-2009=0\Leftrightarrow x=2009.\)

Vậy: \(x=2009.\)