a: \(\left(9x^2-4\right)\left(x+1\right)=\left(3x+2\right)\left(x^2-1\right)\)
=>\(\left(3x-2\right)\left(3x+2\right)\left(x+1\right)-\left(3x+2\right)\left(x-1\right)\left(x+1\right)=0\)
=>(3x+2)(x+1)(3x-2-x+1)=0
=>(3x+2)(x+1)(2x-1)=0
=>\(\left[\begin{array}{l}3x+2=0\\ x+1=0\\ 2x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-\frac23\\ x=-1\\ x=\frac12\end{array}\right.\)
c: \(\left(x-1\right)^2-1+x^2=\left(1-x\right)\left(x+3\right)\)
=>\(x^2-2x+1-1+x^2=-\left(x-1\right)\left(x+3\right)\)
=>\(2x^2-2x+\left(x-1\right)\left(x+3\right)=0\)
=>2x(x-1)+(x-1)(x+3)=0
=>(x-1)(3x+3)=0
=>3(x-1)(x+1)=0
=>(x-1)(x+1)=0
=>\(\left[\begin{array}{l}x-1=0\\ x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1\\ x=-1\end{array}\right.\)
e: \(x^3-7x+6=0\)
=>\(x^3-x-6x+6=0\)
=>\(x\left(x^2-1\right)-6\left(x-1\right)=0\)
=>x(x-1)(x+1)-6(x-1)=0
=>\(\left(x-1\right)\left(x^2+x-6\right)=0\)
=>(x-1)(x+3)(x-2)=0
=>\(\left[\begin{array}{l}x-1=0\\ x+3=0\\ x-2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1\\ x=-3\\ x=2\end{array}\right.\)
g: \(x^5-5x^3+4x=0\)
=>\(x\left(x^4-5x^2+4\right)=0\)
=>\(x\left(x^2-1\right)\left(x^2-4\right)=0\)
=>\(\left[\begin{array}{l}x=0\\ x^2-1=0\\ x^2-4=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x^2=1\\ x^2=4\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\\ x=-1\\ \left[\begin{array}{l}x=2\\ x=-2\end{array}\right.\end{array}\right.\)
