Đáp án:
Giải thích các bước giải:
$\text{xét phương trình : }\\|2x^2 - 3x - 2| = 5a - 8x - x^2 (*)\\\Leftrightarrow 5a = f(x)\\=\left[\begin{matrix}(2x^2 - 3x - 2) + 8x + x^2 \text{ khi }2x^2 - 3x - 2 \ge 0\\-2x^2 + 3x + 2 + 8x + x^2\text{ khi }2x^2 - 3x - 2 < 0\end{matrix}\right.\\=\left[\begin{matrix}3x^2 + 5x - 2\text{ khi } 2x^2 - 3x - 2 \ge 0\\-x^2 + 11x + 2\text{ khi }2x^2 - 3x - 2 < 0\end{matrix}\right.\\\text{ta có BBT}\\\begin{array}{|c|cc|}\hline \text{$x$}&\text{$-\infty$}&\text{$\dfrac{-5}{6}$}&\text{$\dfrac{-1}{2}$}&\text{2}&\text{$+\infty$}\\\hline \text{$$}&+\infty&\text{}&\text{}&\text{}&\text{}+\infty\\&\text{}&\text{$\searrow$}&\text{}&\text{}\nearrow&\text{}\\&\text{$$}&\text{}&\text{}\dfrac{-49}{12}&\text{}&\text{}\\\hline \end{array}\\\text{ta có phương thình $(*)$ , ta đc :}\\5a = \dfrac{-49}{12}\\\Leftrightarrow a = \dfrac{-49}{60}\\ \mathscr{X_{\textit{in hay nhất}}}$
