ข้อสอบคณิต O-NET - 2550

$$\begin{gathered} \mathrm{จากสูตร} \left|x\right| = \left\{\begin{array}{ll}x& ; x\ge 0\\ -x& ; x<0\end{array}\right. \\ \mathrm{จากโจทย์} \frac{1}{\sqrt{2}} = \frac{1}{\sqrt{2}}·\frac{\sqrt{2}}{\sqrt{2}} \\ = \frac{\sqrt{2}}{2} \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} = \left|\frac{1}{2}-\frac{\sqrt{2}}{2}\right|-\left|2-\sqrt{2}\right| \\ = -\left(\frac{1}{2}-\frac{\sqrt{2}}{2}\right)-\left(2-\sqrt{2}\right) \\ = -\frac{1}{2}+\frac{\sqrt{2}}{2}-2+\sqrt{2} \end{gathered}$$

$$\begin{gathered} = \frac{-1+\sqrt{2}-4+2\sqrt{2}}{2} \\ = \frac{-5+3\sqrt{2}}{2} = -\frac{5}{2}+\frac{3\sqrt{2}}{2} \\ = \frac{3\sqrt{2}}{2}-\frac{5}{2} \end{gathered}$$