ข้อสอบคณิต O-NET - 2558

$$\begin{gathered} \mathrm{จาก} A \\ = 3x^2+5x-12 < 0 \\ = \left(3x-4\right)\left(x+3\right) < 0 \end{gathered}$$

$$\begin{gathered} \mathrm{จาก} B \\ = \frac{1}{x-1}-\frac{2}{x} \ge 0 \\ = \frac{x-2\left(x-1\right)}{\left(x-1\right)\left(x\right)} \ge 0 \\ = \frac{x-2x+2}{\left(x-1\right)\left(x\right)} \ge 0 \end{gathered}$$

$$\begin{gathered} = \frac{-x+2}{\left(x-1\right)\left(x\right)} \ge 0 \\ = \frac{-\left(x-2\right)}{\left(x-1\right)\left(x\right)} \ge 0 \\ = \frac{\left(x-2\right)}{\left(x-1\right)\left(x\right)} \le 0 \end{gathered}$$

$$\begin{gathered} \mathrm{เขียน} A \mathrm{และ} B \mathrm{บนเส้นเดียวกัน} \\ \mathrm{จะได้} \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} A-B = \left[0 , 1\right] \\ \mathrm{ดังน้ัน} \mathrm{จำนวนเต็ม} \mathrm{คือ} 0 \mathrm{กับ} 1 \\ \mathrm{ตอบ} 2 \mathrm{ตัว} \mathrm{ข้อ} 3 \end{gathered}$$