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\(\orbr{\begin{cases}x^3=-1\\x^3=8\end{cases}\Rightarrow}\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)
\(x^3-7x+6=0\)
\(\Leftrightarrow x^3-x^2+x^2-x-6x+6=0\)
\(\Leftrightarrow x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2+x-6\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2-2x+3x-6\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[x\left(x-2\right)+3\left(x-2\right)\right]\left(x-1\right)\)
\(\Leftrightarrow\left(x-2\right)\left(x+3\right)\left(x-1\right)=0\)
\(\Rightarrow x=\left\{-3;1;2\right\}\)
\(y^2-7y-8=0\Rightarrow\orbr{\begin{cases}y=-1\\y=8\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\sqrt[3]{-1}=-1\\x=\sqrt[3]{8}=2\end{cases}}\)
6x4+7x3-36x2-7x+6=0
<=> 6x4-2x3+9x3-3x2-33x2+11x-18x+6=0
<=> 2x3(3x-1)+3x2(3x-1)-11x(3x-1)-6(3x-1)=0
<=> (3x-1)(2x3+3x2-11x-6)=0
<=>(3x-1)(2x3-4x2+7x2-14x+3x-6)=0
<=>(3x-1)[2x2(x-2)+7x(x-2)+3(x-2)]=0
<=>(3x-1)(x-2)(2x2+7x+3)=0
<=>(3x-1)(x-2)(2x2+6x+x+3)=0
<=>(3x-1)(x-2)[2x(x+3)+(x+3)]=0
<=>(3x-1)(x-2)(x+3)(2x+1)=0
th1: 3x+1=0 <=> x=\(-\frac{1}{3}\)
th2: x-2=0 <=> x=2
th3: x+3=0 <=> x=-3
th4: 2x+1=0 <=> x=-\(\frac{1}{2}\)
(6x4-12x3)+(193-38x2)+(2x2-4x)-(3x-6)=0
6x^3(x-2)+19x^2(x-2)+2x(x-2)-3(x-2)=0
(x-2)(6x^3+19x^2+2x-3)=0
(x-2)[(6x^3+18x^2)+(x^2+3x)-(x+3)]=0
(x-2)(x+3)(6x^2+x-1)=0
(x-2)(x+3)[(6x^2+3x)-(2x+1)]=0
(x-2)(x+3)(2x+1)(3x-1)=0
⇒ x=2
x=-3
x=-1/2
x=1/3
Thanks