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\(\frac{x+2016}{-3}=-\frac{12}{x+2016}\)
\(\Rightarrow\left(x+2016\right)^2=-3.\left(-12\right)\)
\(\Rightarrow\left(x+2016\right)^2=36\)
\(\Rightarrow\left(x+2016\right)^2=6^2\)
\(\Rightarrow x+2016=6\)
\(\Rightarrow x=6-2016\)
\(\Rightarrow x=-2010\)
ta có :
\(\left(\frac{x}{3}-672\right)+\frac{\left(2016-x\right)}{13}+\frac{\left(x-2016\right)}{17}=0\)
hay \(\left(x-2016\right)\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{17}\right)=0\Leftrightarrow x=2016\)
\(2016x+x\frac{1}{2016}-2016=\frac{1}{2016}\)
\(\Rightarrow2016x-2016+x.\frac{1}{2016}-\frac{1}{2016}=0\)
\(\Rightarrow2016.\left(x-1\right)+\frac{1}{2016}.\left(x-1\right)=0\)
\(\Rightarrow\left(2016+\frac{1}{2016}\right)\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2016+\frac{1}{1016}=0\text{ (loại vì }2016+\frac{1}{2016}>0\text{)}\text{ }\\x-1=0\end{cases}}\)
\(\Rightarrow x=1\)
\(2016x+x\frac{1}{2016}-2016=\frac{1}{2016}\)
\(\Leftrightarrow x\left(2016+\frac{1}{2016}\right)=\frac{1}{2016}+2016\)
\(\Leftrightarrow x=\left(2016+\frac{1}{2016}\right):\left(2016+\frac{1}{2016}\right)\)
\(\Leftrightarrow x=1\)
\(\frac{x+18}{2018}+\frac{x+17}{2017}+\frac{x+16}{2016}=3\)
\(\Rightarrow\frac{x+18}{2018}-1+\frac{x+17}{2017}-1+\frac{x+16}{2016}-1=3-3\)
\(\Rightarrow\frac{x+18-2018}{2018}+\frac{x+17-2017}{2017}+\frac{x+16-2016}{2016}=0\)
\(\Rightarrow\frac{x-2000}{2018}+\frac{x-2000}{2017}+\frac{x-2000}{2016}=0\)
\(\Rightarrow\left(x-2000\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\right)=0\)
Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\ne0\)
=> x - 2000 = 0
=> x = 2000
Ta có :
\(\frac{x+18}{2018}+\frac{x+17}{2017}+\frac{x+16}{2016}=3\)
\(\Leftrightarrow\)\(\left(\frac{x+18}{2018}-1\right)+\left(\frac{x+17}{2017}-1\right)+\left(\frac{x+16}{2016}-1\right)=3-3\) ( trừ hai vế cho 3 )
\(\Leftrightarrow\)\(\frac{x-2000}{2018}+\frac{x-2000}{2017}+\frac{x-2000}{2016}=0\)
\(\Leftrightarrow\)\(\left(x-2000\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\right)=0\)
Vì \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\ne0\)
Nên \(x-2000=0\)
\(\Rightarrow\)\(x=2000\)
Vậy \(x=2000\)
Chúc bạn học tốt ~
Bài làm:
Pt <=> \(\left(\frac{x-1}{2020}-1\right)+\left(\frac{x-3}{2018}-1\right)+\left(\frac{x-5}{2016}-1\right)+\left(\frac{x-7}{2014}-1\right)=4-4\)
\(\Leftrightarrow\frac{x-2021}{2020}+\frac{x-2021}{2018}+\frac{x-2021}{2016}+\frac{x-2021}{2014}=0\)
\(\Rightarrow x-2021=0\Rightarrow x=2021\)
(x+2016)^2=-12.(-3)
(x+2016)^2=36
x+2016=6 hoặc x+2016=-6
x=-2010 ,x=-2022