ข้อสอบคณิต O-NET - 2561

$$\begin{gathered} \mathrm{จากสมบัติของค่าสมบูรณ์} \\ \left|a\right| = \left\{\begin{array}{ll}a& ; a\ge 0\\ -a& ; a<0\end{array}\right. \end{gathered}$$

$$\begin{gathered} \mathrm{จะถอดค่าสมบูรณ์} \left|\frac{4}{\sqrt{5}}-5\right| \mathrm{โดย} \\ \frac{4}{\sqrt{5}} < \frac{5}{\sqrt{5}} < 5 \\ \mathrm{จะได้} \frac{4}{\sqrt{5}}-5 \mathrm{เป็นค่าติดลบ} \\ \left|\frac{4}{\sqrt{5}}-5\right| = - \left(\frac{4}{\sqrt{5}}-5\right) \end{gathered}$$

$$\begin{gathered} \mathrm{ดังนั้น} \left|\frac{4}{\sqrt{5}}-5\right|+\sqrt{5}-\frac{1}{\sqrt{5}} \\ = - \left(\frac{4}{\sqrt{5}}-5\right)+\sqrt{5}-\frac{1}{\sqrt{5}} \\ = -\frac{4}{\sqrt{5}}-5\sqrt{5}-\frac{1}{\sqrt{5}} \\ = \frac{-4+5\sqrt{5}+5-1}{\sqrt{5}} \\ = \frac{5\cancel{\sqrt{5}}}{\cancel{\sqrt{5}}} = 5 \to \mathrm{ตอบ} 1 \end{gathered}$$