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5 tháng 7 2016
Đặt \(g\left(x\right)=x^{2015}-x^{2014}+x^{2013}-...+x-1\)
Dễ thấy: \(f\left(x\right)=x^{2016}-2013\times g\left(x\right)\Rightarrow f\left(2012\right)=2012^{2016}-2013\times g\left(2012\right)\)(a)
Ta có: \(\left(x+1\right)\times g\left(x\right)=\left(x+1\right)\left(x^{2015}-x^{2014}+x^{2013}-...+x-1\right)\)
\(\Rightarrow\left(x+1\right)\times g\left(x\right)=x^{2016}-1\)
\(\Rightarrow\left(2012+1\right)\times g\left(2012\right)=2012^{2016}-1\)hay: \(2013\times g\left(2012\right)=2012^{2016}-1\)
Thay vào (a) ta có: \(f\left(2012\right)=2012^{2016}-\left(2012^{2016}-1\right)=1\).
NG
23 tháng 1 2021
\(\dfrac{x-1}{2016}+\dfrac{x-2}{2015}-\dfrac{x-3}{2014}=\dfrac{x-4}{2013}\)
\(\Leftrightarrow\dfrac{x-1}{2016}+\dfrac{x-2}{2015}=\dfrac{x-4}{2013}+\dfrac{x-3}{2014}\)
\(\Leftrightarrow\left(\dfrac{x-1}{2016}-1\right)+\left(\dfrac{x-2}{2015}-1\right)=\left(\dfrac{x-4}{2013}-1\right)+\left(\dfrac{x-3}{2014}-1\right)\)
\(\Leftrightarrow\dfrac{x-2017}{2016}+\dfrac{x-2017}{2015}=\dfrac{x-2017}{2013}+\dfrac{x-2017}{2014}\)
\(\Leftrightarrow\dfrac{x-2017}{2016}+\dfrac{x-2017}{2015}-\dfrac{x-2017}{2013}-\dfrac{x-2017}{2014}=0\)
\(\Leftrightarrow x-2017.\left(\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}-\dfrac{1}{2013}\right)=0\)
\(\text{Mà }\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}-\dfrac{1}{2103}\ne0\Rightarrow x-2017=0\)
\(\Leftrightarrow x=2017\) \(\text{Vậy }x=2017\)
NH
5 tháng 3 2023
\(\dfrac{x+4}{2014}+\dfrac{x+3}{2015}=\dfrac{x+2}{2016}+\dfrac{x+1}{2017}\)
\(\dfrac{x+4}{2014}+1+\dfrac{x+3}{2015}+1=\dfrac{x+2}{2016}+1+\dfrac{x+1}{2017}+1\)
\(\dfrac{x+2018}{2014}+\dfrac{x+2018}{2015}=\dfrac{x+2018}{2016}+\dfrac{x+2018}{2017}\)
\(\left(x+2018\right)\left(\dfrac{1}{2014}+\dfrac{1}{2015}-\dfrac{1}{2016}-\dfrac{1}{2017}\right)=0\\ x+2018=0\\ x=-2018\)
1 tháng 2 2019
https://dethi.violet.vn/present/showprint/entry_id/11072330
bạn vào link trên sẽ có full đề và đáp án
p/s: nhớ k cho mình nha <3
4 tháng 2 2019
\(\frac{x-2}{4}=-\frac{16}{2-x}\)
\(\Leftrightarrow\frac{x-2}{4}=\frac{16}{x-2}\)
\(\Leftrightarrow\left(x-2\right)^2=4.16=64\)
\(\Leftrightarrow\left(x-2\right)^2=8^2\)
\(\Leftrightarrow\left(x-2-8\right)\left(x-2+8\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(x+6\right)=0\Leftrightarrow\orbr{\begin{cases}x-10=0\\x+6=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-6\end{cases}}}\)
10 tháng 7 2018
Xin lỗi bạn nha dòng cuối mik nhầm ...
\(\Rightarrow x=-2018\)
Vậy x = -2018
10 tháng 7 2018
\(\frac{x+4}{2014}+\frac{x+3}{2015}+\frac{x+2}{2016}+\frac{x+1}{2017}=a\)
\(\Rightarrow\frac{x+4}{2014}+1+\frac{x+3}{2015}+1+\frac{x+2}{2016}+1+\frac{x+1}{2017}+1=a+4\)
\(\frac{x+2018}{2014}+\frac{x+2018}{2015}+\frac{x+2018}{2016}+\frac{x+2018}{2017}=a+4\)
\(\left(x+2018\right).\left(\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}\right)=a+4\)
..
s bk
PH
4
21 tháng 6 2017
\(\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+2}{2016}+1\right)+\left(\frac{x+1}{2017}+1\right)\)
\(\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2016}+\frac{x+2018}{2017}=0\)
\(x+2018.\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}\right)=0\)
\(\Rightarrow x+2018=0\)
\(\Rightarrow x=-2018\)
LM
21 tháng 6 2017
\(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+2}{2016}+\)\(\frac{x+1}{2017}\)
\(\Rightarrow\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+2}{2016}+1\right)+\left(\frac{x+1}{2017}+1\right)\)
\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2016}+\frac{x+2018}{2017}\)
\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2016}-\frac{x+2018}{2017}=0\)
\(\Rightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}\right)=0\)
\(M\text{à:}\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\)
\(\Rightarrow x+2018=0\Rightarrow x=-2018\)