[TEX]\begin{array}{l}y = 2{x^2} - (a + 1)x + b - 2 \\ x = 0 \Rightarrow \left| {y(0)} \right| = \left| {b - 2} \right| \le 1 \Leftrightarrow 1 \le b \le 3 \\ x = 1 \Leftrightarrow \left| {y(1)} \right| = \left| {b - a - 1} \right| \le 1 \Leftrightarrow 0 \le b - a \le 2 \Rightarrow a \ge b - 2 \Rightarrow a \ge - 1(*) \\ x = - 1 \Leftrightarrow \left| {y( - 1)} \right| = \left| {a + 1 + b} \right| \le 1 \Leftrightarrow a + b \le 0 \Rightarrow a \le - b \le - 1(**) \\ (*)\& (**) \Rightarrow a = - 1 \\ b - a \le 2 \Rightarrow b \le a + 2 = 1 \Rightarrow b = 1 \\ \end{array}[/TEX]
thử lại
[TEX]\begin{array}{l}a = - 1;b = 1 \Rightarrow y = 2{x^2} - 1 \\ y' = 4x = 0\Leftrightarrow x = 0 \\ y(0) = - 1 \\ y(1) = 1 \\ y( - 1) = 1 \\ \end{array}[/TEX]
Thỏa mãn