ข้อสอบ PAT 1 - มีนาคม 2555

$$\begin{gathered} \mathrm{จากโจทย์} {\left(\frac{3}{5}\right)}^{(5{\mathrm{x}}^2-23\mathrm{x} +3)}>{\left(\frac{5}{3}\right)}^{(\mathrm{x}+5)} \\ \mathrm{จะได้} {\left(\frac{3}{5}\right)}^{(5{\mathrm{x}}^2-23\mathrm{x} +3)}>{\left(\frac{5}{3}\right)}^{-\mathrm{x}-5} \\ 5{\mathrm{x}}^2-23\mathrm{x} +3<-\mathrm{x}-5 \\ 5{\mathrm{x}}^2-22\mathrm{x} +8<0 \\ \left(5\mathrm{x}-2\right)\left(\mathrm{x}-4\right)<0 \\ \mathrm{x} <\frac{2}{5},4 \end{gathered}$$

$$\begin{gathered} \mathrm{ดังนั้น} \mathrm{A}=\left(\frac{2}{5},4\right) \\ \mathrm{พิจารณาตัวเลือก} \\ \mathbf{ตัวเลือกที่}\mathbf{ }\mathbf{1}\mathbf{ } \left(5\mathrm{x}-1\right)\left(\mathrm{x}-3\right)<0 \\ \mathrm{x} < \frac{1}{5},3 \end{gathered}$$

$$\begin{gathered} \mathrm{A}\not\subset \left(\frac{1}{5},3\right) \mathrm{ผิด} \\ \mathbf{ตัวเลือกที่}\mathbf{ }\mathbf{2} \left(4\mathrm{x}-1\right)\left(\mathrm{x}-4\right)<0 \\ \mathrm{x} < \frac{1}{4},4 \end{gathered}$$

$$\begin{gathered} \mathrm{A}\subset \left(\frac{1}{4},4\right) \mathrm{ถูก} \\ \mathbf{ตัวเลือกที่}\mathbf{ }\mathbf{3} \left(2\mathrm{x}-1\right)\left(\mathrm{x}-5\right)<0 \\ \mathrm{x} <\frac{1}{2},5 \end{gathered}$$

$$\begin{gathered} \mathrm{A}\not\subset \left(\frac{1}{2},5\right) \mathrm{ผิด} \\ \mathbf{ตัวเลือกที่}\mathbf{ }\mathbf{4} \left|\mathrm{x}-1\right|<2 \\ -2<\mathrm{x}-1<2 \\ -1<\mathrm{x}<3 \end{gathered}$$

$\mathrm{A}\not\subset \left(-1,3\right) \mathrm{ผิด}$