a: \(\Leftrightarrow2x^4-4x^3-5x^3+10x^2+4x^2-8x-x+2=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x^3-5x^2+4x-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x^3-2x^2-3x^2+3x+x-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-1\right)\left(2x^2-3x+1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-1\right)^2\cdot\left(2x-1\right)=0\)
hay \(x\in\left\{2;1;\dfrac{1}{2}\right\}\)
b: \(\Leftrightarrow6x^4+12x^3+13x^3+26x^2-14x^2-28x+3x+6=0\)
\(\Leftrightarrow\left(x+2\right)\left(6x^3+13x^2-14x+3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(6x^3+18x^2-5x^2-15x+x+3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)\left(6x^2-5x+1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)\left(2x-1\right)\left(3x-1\right)=0\)
hay \(x\in\left\{-2;-3;\dfrac{1}{2};\dfrac{1}{3}\right\}\)
\(a,PT\Leftrightarrow2x^3\left(x-1\right)-7x^2\left(x-1\right)+7x\left(x-1\right)-2\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(2x^3-7x^2+7x-2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[2\left(x^3-1\right)-7x\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left[2\left(x-1\right)\left(x^2+x+1\right)-7x\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x-1\right)\left(2x^2+2x+2-7x\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(2x^2-5x+2\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(x-2\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=\dfrac{1}{2}\end{matrix}\right.\)
Vậy: \(S=\left\{1;2;\dfrac{1}{2}\right\}\)
\(b,PT\Leftrightarrow6x^3\left(x+2\right)+13x^2\left(x+2\right)-14x\left(x+2\right)+3\left(x+2\right)=0\Leftrightarrow\left(x+2\right)\left(6x^3+13x^2-14x+3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left[6x^2\left(x+3\right)-5x\left(x+3\right)+\left(x+3\right)\right]=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)\left(6x^2-5x+1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)\left(2x-1\right)\left(3x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-3\\x=\dfrac{1}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{-2;-3;\dfrac{1}{2};\dfrac{1}{3}\right\}\)
