a, \(5x^2-4\left(x^2-2x+1\right)-5=0\)
\(\Rightarrow5x^2-4x^2+8x-4-5=0\)
\(\Rightarrow x^2-x+9x-9=0\)
\(\Rightarrow x\left(x-1\right)+9\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x+9\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-9\end{matrix}\right.\)
b, \(\left(x^2-9\right)^2-\left(x-3\right)^2=0\)
\(\Rightarrow\left(x^2-9-x+3\right)\left(x^2-9+x-3\right)=0\)
\(\Rightarrow\left(x^2-x-6\right)\left(x^2+x-12\right)=0\)
\(\Rightarrow\left(x^2-3x+2x-6\right)\left(x^2+4x-3x-12\right)=0\)
\(\Rightarrow\left[x\left(x-3\right)+2\left(x-3\right)\right]\left[x\left(x+4\right)-3\left(x+4\right)\right]=0\)
\(\Rightarrow\left(x-3\right)\left(x+2\right)\left(x+4\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=-4\end{matrix}\right.\)
c, \(x^3-3x+2=0\)
\(\Rightarrow x^3+2x^2-2x^2-4x+x+2=0\)
\(\Rightarrow x^2\left(x+2\right)-2x\left(x+2\right)+\left(x+2\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x^2-2x+1\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x-1\right)^2=0\)
\(\Rightarrow\left[{}\begin{matrix}x+2=0\\\left(x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)
a, 5x2−4(x2−2x+1)−5=05x2−4(x2−2x+1)−5=0
⇒5x2−4x2+8x−4−5=0⇒5x2−4x2+8x−4−5=0
⇒x2−x+9x−9=0⇒x2−x+9x−9=0
⇒x(x−1)+9(x−1)=0⇒x(x−1)+9(x−1)=0
⇒(x−1)(x+9)=0⇒(x−1)(x+9)=0
⇒[x−1=0x+9=0⇒[x=1x=−9⇒[x−1=0x+9=0⇒[x=1x=−9
b, (x2−9)2−(x−3)2=0(x2−9)2−(x−3)2=0
⇒(x2−9−x+3)(x2−9+x−3)=0⇒(x2−9−x+3)(x2−9+x−3)=0
⇒(x2−x−6)(x2+x−12)=0⇒(x2−x−6)(x2+x−12)=0
⇒(x2−3x+2x−6)(x2+4x−3x−12)=0⇒(x2−3x+2x−6)(x2+4x−3x−12)=0
⇒[x(x−3)+2(x−3)][x(x+4)−3(x+4)]=0⇒[x(x−3)+2(x−3)][x(x+4)−3(x+4)]=0
⇒(x−3)(x+2)(x+4)(x−3)=0⇒(x−3)(x+2)(x+4)(x−3)=0
⇒⎡⎢⎣x−3=0x+2=0x+4=0⇒⎡⎢⎣x=3x=−2x=−4⇒[x−3=0x+2=0x+4=0⇒[x=3x=−2x=−4
c, x3−3x+2=0x3−3x+2=0
⇒x3+2x2−2x2−4x+x+2=0⇒x3+2x2−2x2−4x+x+2=0
⇒x2(x+2)−2x(x+2)+(x+2)=0⇒x2(x+2)−2x(x+2)+(x+2)=0
⇒(x+2)(x2−2x+1)=0⇒(x+2)(x2−2x+1)=0
⇒(x+2)(x−1)2=0⇒(x+2)(x−1)2=0
⇒[x+2=0(x−1)2=0⇒[x=−2x=1⇒[x+2=0(x−1)2=0⇒[x=−2x=1
