a)$(x-5)^{3}$-x+5=0
⇔$(x-5)^{3}$-(x-5)=0
⇔(x-5)[$(x-5)^{2}$-1]=0
⇔(x-5)(x²-10x+25-1)=0
⇔(x-5)(x²-10x+24)=0
⇔(x-5)(x-6)(x-4)=0
⇔\(\left[ \begin{array}{l}x-5=0\\x-6=0\\x-4=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=5\\x=6\\x=4\end{array} \right.\)
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b)x²(x-5)+5-x=0
⇔x²(x-5)-(x-5)=0
⇔(x²-1)(x-5)=0
⇔(x+1)(x-1)(x-5)=0
⇔\(\left[ \begin{array}{l}x+1=0\\x-1=0\\x-5=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-1\\x=1\\x=5\end{array} \right.\)
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c)3x(x-1)+x-1=0
⇔3x(x-1)+(x-1)=0
⇔(3x+1)(x-1)=0
⇔\(\left[ \begin{array}{l}3x+1=0\\x-1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-$\frac{1}{3}$\\x=1\end{array} \right.\)
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d)(x³-x²)-4x²+8x-4=0
⇔(x³-x²)-(4x²-8x+4)=0
⇔x²(x-1)-4(x-1)²=0
⇔(x-1)[x²-4(x-1)]=0
⇔(x-1)(x²-4x+4)=0
⇔(x-1)(x-2)²=0
⇔\(\left[ \begin{array}{l}x-1=0\\x-2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
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