ข้อสอบคณิต O-NET - 2559

$$\begin{gathered} \mathrm{จากโจทย์} \mathrm{จัดรูปสมการ} \\ \mathrm{จะได้} \frac{x^{{\displaystyle \frac{1}{2}}}-\sqrt{3}{x}^{-{\displaystyle \frac{1}{2}}}}{x} = \frac{\sqrt{x}-{\displaystyle \frac{\sqrt{3}}{\sqrt{x}}}}{x} \\ = \frac{\frac{\sqrt{x}-\sqrt{3}}{\sqrt{x}}}{x} \\ = \frac{x-\sqrt{3}}{x\sqrt{x}} \\ = \frac{x-\sqrt{3}}{x^{{\displaystyle \frac{3}{2}}}} \end{gathered}$$

$$\begin{gathered} \mathrm{โจทย์ให้} x = 1+\sqrt{3} \\ \mathrm{จะได้} = \frac{1+\sqrt{3}-\sqrt{3}}{{\left(1+\sqrt{3}\right)}^{{\displaystyle \frac{3}{2}}}} \\ = \frac{1}{{\left(1+\sqrt{3}\right)}^{\frac{3}{2}}} \\ = {\left(1+\sqrt{3}\right)}^{-\frac{3}{2}} \end{gathered}$$