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Bài làm:
Pt <=> \(\left(\frac{x-1}{2020}-1\right)+\left(\frac{x-3}{2018}-1\right)+\left(\frac{x-5}{2016}-1\right)+\left(\frac{x-7}{2014}-1\right)=4-4\)
\(\Leftrightarrow\frac{x-2021}{2020}+\frac{x-2021}{2018}+\frac{x-2021}{2016}+\frac{x-2021}{2014}=0\)
\(\Rightarrow x-2021=0\Rightarrow x=2021\)
Ta có :\(\frac{x-1}{2020}+\frac{x-3}{2018}+\frac{x-5}{2016}+\frac{x-7}{2014}=4\)
=> \(\left(\frac{x-1}{2020}-1\right)+\left(\frac{x-3}{2018}-1\right)+\left(\frac{x-5}{2016}-1\right)+\left(\frac{x-7}{2014}-1\right)=0\)
=> \(\frac{x-2021}{2020}+\frac{x-2021}{2018}+\frac{x-2021}{2016}+\frac{x-2021}{2014}=0\)
=> \(\left(x-2021\right)\left(\frac{1}{2020}+\frac{1}{2018}+\frac{1}{2016}+\frac{1}{2014}\right)=0\)
Vì \(\frac{1}{2020}+\frac{1}{2018}+\frac{1}{2016}+\frac{1}{2014}\ne0\)
=> x - 2021 = 0
=> x = 2021
Vậy x = 2021
Bài làm :
Ta có :
\(\frac{x-1}{2020}+\frac{x-3}{2018}+\frac{x-5}{2016}+\frac{x-7}{2014}=4\)
\(\Leftrightarrow\left(\frac{x-1}{2020}-1\right)+\left(\frac{x-3}{2018}-1\right)+\left(\frac{x-5}{2016}-1\right)+\left(\frac{x-7}{2014}-1\right)=0\)
\(\Leftrightarrow\frac{x-2021}{2020}+\frac{x-2021}{2018}+\frac{x-2021}{2016}+\frac{x-2021}{2014}=0\)
\(\Leftrightarrow\left(x-2021\right)\left(\frac{1}{2020}+\frac{1}{2018}+\frac{1}{2016}+\frac{1}{2014}\right)=0\)
\(\text{Vì :}\frac{1}{2020}+\frac{1}{2018}+\frac{1}{2016}+\frac{1}{2014}>0\)
\(\Rightarrow x-2021=0\)
\(\Rightarrow x=2021\)
Vậy x=2021
Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!