x-2/2017+x-3/2016+x-4/2015+…+x-10/2009=9 01/11/2021 Bởi Adalynn x-2/2017+x-3/2016+x-4/2015+…+x-10/2009=9
Ta có $\dfrac{x-2}{2017} + \dfrac{x-3}{2016} + \dfrac{x-4}{2015} + \cdots + \dfrac{x-10}{2009} = 9$ $<-> \left( \dfrac{x-2}{2017} – 1 \right) + \left( \dfrac{x-3}{2016} – 1 \right) + \left( \dfrac{x-4}{2015} – 1 \right) + \cdots + \left( \dfrac{x-10}{2009} – 1 \right) = 0$ $<-> \dfrac{x-2-2017}{2017 }+ \dfrac{x-3-2016}{2016} + \dfrac{x-4-2015}{2015} + \cdots + \dfrac{x-10-2009}{2009} = 0$ $<-> (x-2019) \left( \dfrac{1}{2017} + \dfrac{1}{2016} + \dfrac{1}{2015} + \cdots + \dfrac{1}{2009} \right) = 0$ $<-> x – 2019 = 0$ $<-> x = 2019$ Vậy $x = 2019$. Bình luận
Ta có
$\dfrac{x-2}{2017} + \dfrac{x-3}{2016} + \dfrac{x-4}{2015} + \cdots + \dfrac{x-10}{2009} = 9$
$<-> \left( \dfrac{x-2}{2017} – 1 \right) + \left( \dfrac{x-3}{2016} – 1 \right) + \left( \dfrac{x-4}{2015} – 1 \right) + \cdots + \left( \dfrac{x-10}{2009} – 1 \right) = 0$
$<-> \dfrac{x-2-2017}{2017 }+ \dfrac{x-3-2016}{2016} + \dfrac{x-4-2015}{2015} + \cdots + \dfrac{x-10-2009}{2009} = 0$
$<-> (x-2019) \left( \dfrac{1}{2017} + \dfrac{1}{2016} + \dfrac{1}{2015} + \cdots + \dfrac{1}{2009} \right) = 0$
$<-> x – 2019 = 0$
$<-> x = 2019$
Vậy $x = 2019$.