ข้อสอบ A-Level คณิตประยุกต์ 1 ปี 2555 (วิชาสามัญเก่า)

$$\begin{gathered} \mathrm{จากโจทย์} \mathrm{ถ้า} \mathrm{ห}.\mathrm{ร}.\mathrm{ม}. (\mathrm{a}, \mathrm{b}) = 5 \\ \mathrm{กำหนดให้} \mathrm{a} = 5\mathrm{x} , \mathrm{b} = 5\mathrm{y} \to \boxed{1} \end{gathered}$$

$$\begin{gathered} \mathrm{จากโจทย์} \mathrm{ab} – 25\mathrm{a} – 25\mathrm{b} = 1575 \\ \left(5\mathrm{x}\right)\left(5\mathrm{y}\right) – 25\left(5\mathrm{x}\right) – 25\left(5\mathrm{y}\right) = 1575 \\ 25\mathrm{xy} – 125\mathrm{x} – 125\mathrm{y} = 1575 \\ \cancel{25}(\mathrm{xy} – 5\mathrm{x} – 5\mathrm{y}) = \cancel{25}\left(63\right) \\ \mathrm{xy} – 5\mathrm{x} – 5\mathrm{y} = 63 ;+25 \mathrm{ทั้ง} 2 \mathrm{ข้าง} \\ \mathrm{xy} – 5\mathrm{x} – 5\mathrm{y} + 25 = 63 + 25 \\ \mathrm{x}(\mathrm{y} – 5) – 5(\mathrm{y} – 5) = 88 \\ (\mathrm{x} – 5)(\mathrm{y} – 5) = 11\left(8\right) \end{gathered}$$

$$\begin{gathered} \mathrm{แสดงว่า} \mathrm{x} – 5 = 11 \mathrm{และ} \mathrm{y} – 5 = 8 \\ \mathrm{x} = 16 \mathrm{y} = 13 \\ \mathrm{จาก} \boxed{1} \mathrm{จะได้} \mathrm{a} = 5\mathrm{x} \mathrm{b} = 5\mathrm{y} \\ \mathrm{a} = 5\left(16\right) \mathrm{b} = 5\left(13\right) \\ \mathrm{a} = 80 \mathrm{b} = 65 \\ \mathrm{ดังนั้น} \left|\mathrm{a}-\mathrm{b}\right|=\left|80-65\right| \\ =\left|15\right| \\ =15 \end{gathered}$$