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a )
\(5x\left(x-3\right)+7\left(x-3\right)=0\)
\(\Rightarrow\left(5x+7\right)\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}5x+7=0\\x-3=0\end{cases}\Rightarrow\orbr{\begin{cases}5x=-7\\x=3\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{7}{5}\\x=3\end{cases}}}\)
Vậy ...
b )
\(x^{2017}=x^{2018}\)
\(\Rightarrow x^{2017}-x^{2018}=0\)
\(\Rightarrow x^{2017}\left(1-x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^{2017}=0\\1-x=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)
Vậy ...
c )
\(2x^2=x\)
\(\Rightarrow2x^2:x=1\)
\(\Rightarrow2x=1\)
\(\Rightarrow x=\frac{1}{2}\)
Vậy ...
e )
\(x^5=x^4\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}\)( làm tương tự như phần b )
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a: \(8x\left(x-2017\right)-2x+4034=0\)
\(\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\)
x+(x+1)+(x+2)+(x+3)+...+(x+2016)=2017
( x + x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 2016 ) = 2017
2017x + 2033136 = 2017
2017x = 2017 - 2033136
2017x = -2031119
x = -2031119 : 2017
x = -1007
Ta có : x + (x + 1) + (x + 2) + (x + 3) +......+ (x + 2016) = 2017
=> (x + x + x + ..... + x) + (1 + 2 + 3 + .... + 2016) = 2017
=> 2017x + 2033136 = 2017
=> 2017x = 2017 - 2033136
=> 2017x = -203119
=> x = -203119 : 2017
=> x = -1007
a) \(x\left(x-2017\right)=x-2017\)
\(\Rightarrow x\left(x-2017\right)-\left(x-2017\right)=0\\ \Rightarrow\left(x-1\right)\left(x-2017\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-1=0\\x-2017=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=2017\end{matrix}\right.\)
b) \(5x\left(x-1\right)=1-x\)
\(\Rightarrow5x\left(x-1\right)=-\left(x-1\right)\\ \Rightarrow5x\left(x-1\right)+\left(x-1\right)=0\\ \Rightarrow\left(5x+1\right)\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}5x+1=0\\x-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{5}\\x=1\end{matrix}\right.\)
c) \(\left(3x-4\right)^2-\left(x+1\right)^2=0\)
\(\Rightarrow\left(3x-4-x-1\right)\left(3x-4+x+1\right)=0\\ \Rightarrow\left(2x-5\right)\left(4x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x-5=0\\4x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{3}{4}\end{matrix}\right.\)