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Ta có \(\frac{2015}{2016}.x+\frac{2016}{2017}.x+\frac{2017}{2018}.x=\frac{2018}{2019}.x\)
<=>\(\frac{2015}{2016}.x+\frac{2016}{2017}.x+\frac{2017}{2018}x-\frac{2018}{2019}x=0\)
<=>x\(\left(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}-\frac{2018}{2019}\right)=0\)
Vì \(\frac{2015}{2016}+\frac{2016}{2017}+\frac{2017}{2018}-\frac{2018}{2019}\) không thể bằng 0
Vậy x=0
Ta có 1 nghiệm thỏa mãn S=\(\left\{0\right\}\)
Hình như đề sai dấu, mình sửa lại rồi!
\(\frac{x-1}{2017}+\frac{x-2}{2016}+\frac{x-3}{2015}+...+\frac{x-2017}{1}=2017\)
\(\Leftrightarrow\) \(\frac{x-1}{2017}-1+\frac{x-2}{2016}-1+\frac{x-3}{2015}-1+...+\frac{x-2017}{1}-1=0\)
\(\Leftrightarrow\) \(\frac{x-2018}{2017}+\frac{x-2018}{2016}+\frac{x-2018}{2015}+...+\frac{x-2018}{1}=0\)
\(\Leftrightarrow\) (x - 2018)\(\left(\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}+...+1\right)=0\)
\(\Leftrightarrow\) x - 2018 = 0
\(\Leftrightarrow\) x = 2018
Vậy S = {2018}
Chúc bn học tốt!!
Hình như đề sai dấu, mình sửa lại rồi!
\(\frac{x-1}{2017}+\frac{x-2}{2016}+\frac{x-3}{2015}+...+\frac{x-2017}{1}=2017\)
\(\Leftrightarrow\) \(\frac{x-1}{2017}-1+\frac{x-2}{2016}-1+\frac{x-3}{2015}-1+...+\frac{x-2017}{1}-1=0\)
\(\Leftrightarrow\) \(\frac{x-2018}{2017}+\frac{x-2018}{2016}+\frac{x-2018}{2015}+...+\frac{x-2018}{1}=0\)
\(\Leftrightarrow\) (x - 2018)\(\left(\frac{1}{2017}+\frac{1}{2016}+\frac{1}{2015}+...+1\right)=0\)
\(\Leftrightarrow\) x - 2018 = 0
\(\Leftrightarrow\) x = 2018
Vậy S = {2018}
Chúc bn học tốt!!
Cho A=\(\frac{2017-2016}{2017+2016}\)và B=\(\frac{2017^2-2016^2}{2017^2+2016^2}\)
Hãy so sánh A và B
\(\Leftrightarrow\frac{x-3}{2016}-1=\left(\frac{x-2}{2017}-1\right)+\left(\frac{x-1}{2018}-1\right)\)
\(\Leftrightarrow\frac{x-3-2016}{2016}=\frac{x-2-2017}{2017}+\frac{x-1-2018}{2018}\)
\(\Leftrightarrow\frac{x-2019}{2016}-\frac{x-2019}{2017}-\frac{x-2019}{2018}=0\)
\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\right)=0\)
Vì \(\frac{1}{2016}-\frac{1}{2017}-\frac{1}{2018}\ne0\) ( không tin cứ bấm máy tính mà xem =)) )
\(\Rightarrow x-2019=0\Rightarrow x=2019\)
\(\frac{x-2}{2016}+\frac{x-3}{2017}+\frac{x-4}{2018}+3=0\\ \Leftrightarrow\left(\frac{x-2}{2016}+1\right)+\left(\frac{x-3}{2017}+1\right)+\left(\frac{x-4}{2018}+1\right)=0\\ \Leftrightarrow\frac{x+2014}{2016}+\frac{x+2014}{2017}+\frac{x+2014}{2018}=0\\ \Leftrightarrow\left(x+2014\right)\left(\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\right)=0\\ Vì\frac{1}{2016}+\frac{1}{2017}+\frac{1}{2018}\ne0\\ \Rightarrow x+2014=0\\ \Leftrightarrow x=-2014\\ Vậy...\)
\(\frac{2016-x}{2017}\)+\(\frac{2017-x}{2016}\)+2=\(\frac{2016}{2017-x}\)+\(\frac{2017}{2016-x}\)+2
\(\frac{4033-x}{2017}\)+\(\frac{4033-x}{2016}\)=\(\frac{4033-x}{2017-x}\)+\(\frac{4033-x}{2016-x}\)
(4033-x)(\(\frac{1}{2017}\)+\(\frac{1}{2016}\)-\(\frac{1}{2017-x}\)-\(\frac{1}{2016-x}\))=0
=>\(\hept{\begin{cases}4033-x=0\\\frac{1}{2017}+\frac{1}{2016}-\frac{1}{2017-x}-\frac{1}{2016-x}\end{cases}}=0\)
=>x=4033
x=0
mk ko biết xin lỗi bạn nha!!!
mk ko biết xin lỗi bạn nha!!!
mk ko biết xin lỗi bạn nha!!!
mk ko biết xin lỗi bạn nha!!!