1: \(3x^2-9x=0\)
=>\(3x\cdot x-3x\cdot3=0\)
=>\(3x\left(x-3\right)=0\)
=>x(x-3)=0
=>\(\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
2: \(x^2\left(4-x\right)+9\left(4-x\right)=0\)
=>\(\left(4-x\right)\left(x^2+9\right)=0\)
mà \(x^2+9>=9>0\forall x\)
nên 4-x=0
=>x=4
3: \(x\left(x-2\right)+x-2=0\)
=>\(x\left(x-2\right)+\left(x-2\right)=0\)
=>\(\left(x-2\right)\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
4: \(\left(2x-3\right)^2-\left(2x-3\right)\left(x+2\right)=0\)
=>\(\left(2x-3\right)\left(2x-3-x-2\right)=0\)
=>\(\left(2x-3\right)\left(x-5\right)=0\)
=>\(\left[{}\begin{matrix}2x-3=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=5\end{matrix}\right.\)
5: \(\left(x+1\right)^2=x+1\)
=>\(\left(x+1\right)^2-\left(x+1\right)=0\)
=>\(\left(x+1\right)\left(x+1-1\right)=0\)
=>\(x\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
6: \(x\left(x-1\right)+4\left(1-x\right)=0\)
=>\(x\left(x-1\right)-4\left(x-1\right)=0\)
=>\(\left(x-1\right)\left(x-4\right)=0\)
=>\(\left[{}\begin{matrix}x-1=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\)
7: \(5x\left(x-2\right)-x+2=0\)
=>\(5x\left(x-2\right)-\left(x-2\right)=0\)
=>\(\left(x-2\right)\left(5x-1\right)=0\)
=>\(\left[{}\begin{matrix}x-2=0\\5x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{5}\end{matrix}\right.\)
8: \(4x\left(x-2018\right)-x+2018=0\)
=>\(4x\left(x-2018\right)-\left(x-2018\right)=0\)
=>\(\left(x-2018\right)\left(4x-1\right)=0\)
=>\(\left[{}\begin{matrix}x-2018=0\\4x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2018\\x=\dfrac{1}{4}\end{matrix}\right.\)
9: \(6x\left(x^2-2\right)-\left(2-x^2\right)=0\)
=>\(6x\left(x^2-2\right)+\left(x^2-2\right)=0\)
=>\(\left(x^2-2\right)\left(6x+1\right)=0\)
=>\(\left[{}\begin{matrix}x^2-2=0\\6x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2=2\\6x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\pm\sqrt{2}\\x=-\dfrac{1}{6}\end{matrix}\right.\)
10: \(\left(2x-3\right)^2-\left(3-2x\right)\left(x+5\right)=0\)
=>\(\left(2x-3\right)^2+\left(2x-3\right)\left(x+5\right)=0\)
=>\(\left(2x-3\right)\left(2x-3+x+5\right)=0\)
=>\(\left(2x-3\right)\left(3x+2\right)=0\)
=>\(\left[{}\begin{matrix}2x-3=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{2}{3}\end{matrix}\right.\)
11: \(\left(x+1\right)^2-4=0\)
=>\(\left(x+1+2\right)\left(x+1-2\right)=0\)
=>\(\left(x+3\right)\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}x+3=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)
12: \(9x^2-16\left(x-1\right)^2=0\)
=>\(\left(3x\right)^2-\left[4\left(x-1\right)\right]^2=0\)
=>\(\left(3x\right)^2-\left(4x-4\right)^2=0\)
=>\(\left(3x-4x+4\right)\left(3x+4x-4\right)=0\)
=>\(\left(-x+4\right)\left(7x-4\right)=0\)
=>\(\left[{}\begin{matrix}-x+4=0\\7x-4=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}-x=-4\\7x=4\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=4\\x=\dfrac{4}{7}\end{matrix}\right.\)
13: \(x^3-3x^2+3x-1=0\)
=>\(x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3=0\)
=>\(\left(x-1\right)^3=0\)
=>x-1=0
=>x=1
14: \(x^3+3x^2+3x+1=0\)
=>\(x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=0\)
=>\(\left(x+1\right)^3=0\)
=>x+1=0
=>x=-1
15: \(25x^2+10x+1=0\)
=>\(\left(5x\right)^2+2\cdot5x\cdot1+1^2=0\)
=>\(\left(5x+1\right)^2=0\)
=>5x+1=0
=>x=-1/5
16: \(x^2-6x+9=0\)
=>\(x^2-2\cdot x\cdot3+3^2=0\)
=>\(\left(x-3\right)^2=0\)
=>x-3=0
=>x=3
17: \(25x^2-16=0\)
=>\(\left(5x\right)^2-4^2=0\)
=>\(\left(5x-4\right)\left(5x+4\right)=0\)
=>\(\left[{}\begin{matrix}5x-4=0\\5x+4=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
18: \(16x^2-81=0\)
=>\(\left(4x\right)^2-9^2=0\)
=>\(\left(4x+9\right)\left(4x-9\right)=0\)
=>\(\left[{}\begin{matrix}4x+9=0\\4x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{9}{4}\\x=\dfrac{9}{4}\end{matrix}\right.\)
\(1,3x^2-9x=0\\ \Leftrightarrow3x\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\\ --\\ 2,x^2\left(4-x\right)+9\left(4-x\right)=0\\ \Leftrightarrow\left(x^2+9\right)\left(4-x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+9=0\\4-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2=-9\left(l\right)\\x=4\left(n\right)\end{matrix}\right.\Leftrightarrow x=4\\ --\\ 3,x\left(x-2\right)+x-2=0\\ \Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
\(4,\left(2x-3\right)^2-\left(2x-3\right)\left(x+2\right)=0\\ \Leftrightarrow\left(2x-3\right)\left(2x-3-x-2\right)=0\\ \Leftrightarrow\left(2x-3\right)\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x-3=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=5\end{matrix}\right.\\ --\\ 5,\left(x+1\right)^2=x+1\\ \Leftrightarrow x^2+2x+1-x-1=0\\ \Leftrightarrow x^2+x=0\\ \Leftrightarrow x\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\\ --\\ 6,x\left(x-1\right)+4\left(1-x\right)=0\\ \Leftrightarrow x\left(x-1\right)-4\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=1\end{matrix}\right.\)
\(16,x^2-6x+9=0\\ \Leftrightarrow x^2-2.x.3+3^2=0\\ \Leftrightarrow\left(x-3\right)^2=0\\ \Leftrightarrow x-3=0\Leftrightarrow x=3\\ --\\ 17,25x^2-16=0\\ \Leftrightarrow\left(5x\right)^2-4^2=0\\ \Leftrightarrow\left(5x-4\right)\left(5x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}5x-4=0\\5x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=4\\5x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\\ --\\ 18,16x^2-81=0\\ \Leftrightarrow\left(4x\right)^2-9^2=0\\ \Leftrightarrow\left(4x-9\right)\left(4x+9\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}4x-9=0\\4x+9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=9\\4x=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=-\dfrac{9}{4}\end{matrix}\right.\)
\(7,5x\left(x-2\right)-x+2=0\\ \Leftrightarrow5x\left(x-2\right)-\left(x-2\right)=0\\ \Leftrightarrow\left(5x-1\right)\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}5x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\\x=2\end{matrix}\right.\\ --\\ 8,4x\left(x-2018\right)-x+2018=0\\ \Leftrightarrow4x\left(x-2018\right)-\left(x-2018\right)=0\\ \Leftrightarrow\left(4x-1\right)\left(x-2018\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}4x-1=0\\x-2018=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=2018\end{matrix}\right.\\ --\\ 9,6x\left(x^2-2\right)-\left(2-x^2\right)=0\\ \Leftrightarrow6x\left(x^2-2\right)+\left(x^2-2\right)=0\\ \Leftrightarrow\left(x^2-2\right)\left(6x+1\right)=0\\ \Leftrightarrow\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\left(6x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-\sqrt{2}=0\\x+\sqrt{2}=0\\6x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\\x=-\dfrac{1}{6}\end{matrix}\right.\)
