Tìm x biết ​rằng \( (2{x^4} - 3{x^3} + {x^2}):\left( { - \frac{1}{2}{x^2}} \right) + 4{(x - 1)^2} = 0\)

* Hướng dẫn giải

Ta có:

\(\begin{array}{l} \left( {2{x^4} - 3{x^3} + {x^2}} \right):\left( { - \frac{1}{2}{x^2}} \right) + 4{\left( {x - 1} \right)^2} = 0\\ \Leftrightarrow 2{x^4}:\left( { - \frac{1}{2}{x^2}} \right) - 3{x^3}:\left( { - \frac{1}{2}{x^2}} \right) + {x^2}:\left( { - \frac{1}{2}{x^2}} \right) + 4\left( {{x^2} - 2x + 1} \right) = 0\\ \begin{array}{*{20}{l}} { \Leftrightarrow - 4{x^2} + 6x - 2 + 4{x^2} - 8x + 4 = 0}\\ { \Leftrightarrow - 2x + 2 = 0}\\ { \Leftrightarrow x = 1} \end{array} \end{array}\)