a) \(x^3-9x=0\)
\(\Leftrightarrow x\left(x^2-9\right)=0\)
\(\Leftrightarrow x\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x-3=0\\x+3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=3\\x=-3\end{array}\right.\)
b) \(\left(5-2x\right)\left(2x+7\right)=4x^2-25\)
\(\Leftrightarrow-\left(2x-5\right)\left(2x+7\right)-\left(2x-5\right)\left(2x+5\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(-2x-7-2x-5\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(-4x-12\right)=0\)
\(\Leftrightarrow-4\left(2x-5\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x-5=0\\x+3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{5}{2}\\x=-3\end{array}\right.\)
c) \(x^2-2x-3=0\)
\(\Leftrightarrow x^2+x-3x-3=0\)
\(\Leftrightarrow x\left(x+1\right)-3\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x+1=0\\x-3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-1\\x=3\end{array}\right.\)
c) \(2x^2+7x=4\)
\(\Leftrightarrow2x^2+7x-4=0\)
\(\Leftrightarrow2x^2+8x-x-4=0\)
\(\Leftrightarrow2x\left(x+4\right)-\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x+4=0\\2x-1=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-4\\x=\frac{1}{2}\end{array}\right.\)
e) \(3x^2-7x+2=0\)
\(\Leftrightarrow3x^2-x-6x+2=0\)
\(\Leftrightarrow x\left(3x-1\right)-2\left(3x-1\right)=0\)
\(\Leftrightarrow\left(3x-1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}3x-1=0\\x-1=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{1}{3}\\x=1\end{array}\right.\)
