Đáp án:
\(\left[ \begin{array}{l}
x = 1\\
x = 2\\
x = - 1\\
x = \frac{1}{2}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
2{x^5} - 3{x^4} - 5{x^3} + 5{x^2} + 3x - 2 = 0\\
\leftrightarrow 2{x^5} - 2{x^4} - {x^4} + {x^3} - 6{x^3} + 6{x^2} - {x^2} + x + 2x - 2 = 0\\
\leftrightarrow 2{x^4}(x - 1) - {x^3}(x - 1) - 6{x^2}(x - 1) - x(x - 1) + 2(x - 1) = 0\\
\leftrightarrow (x - 1)(2{x^4} - {x^3} - 6{x^2} - x + 2) = 0\\
\leftrightarrow (x - 1)(2{x^4} - 4{x^3} + 3{x^3} - 6{x^2} - x + 2) = 0\\
\leftrightarrow (x - 1)\left[ {2{x^3}(x - 2) + 3{x^2}(x - 2) - (x - 2)} \right] = 0\\
\leftrightarrow (x - 1)(x - 2)(2{x^3} + 3{x^2} - 1) = 0\\
\leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = 2\\
2{x^3} + 3{x^2} - 1 = 0
\end{array} \right. \leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = 2\\
x = - 1\\
x = \frac{1}{2}
\end{array} \right.
\end{array}\)
