Giải thích các bước giải:
$C = \sqrt{x + 2\sqrt{x - 1}} + \sqrt{x - 2\sqrt{x - 1}}$
$\Rightarrow C^{2} = x + 2\sqrt{x - 1} + x - 2\sqrt{x - 1} + 2\sqrt{\left ( x + 2\sqrt{x - 1} \right )\left ( x - 2\sqrt{x - 1} \right )}$
$= 2x + 2\sqrt{x^{2} - 4x + 4}$
$= 2x + 2\sqrt{\left ( x - 2 \right )^{2}}$
$= 2x + 2\left | x - 2 \right | \left ( 1 \right )$
+ Nếu $x - 2 \geq 0 \Leftrightarrow x \geq 2$ thì:
$\left ( 1 \right ) \Leftrightarrow 2x + 2\left ( x - 2 \right ) = 2x + 2x - 4 = 4x - 4 = 4\left ( x - 1 \right )$
$\Rightarrow C = \sqrt{4\left ( x - 1 \right )} = 2\sqrt{x - 1}$
+ Nếu $x - 2 < 0 \Leftrightarrow x < 2$ thì:
$\left ( 1 \right ) \Leftrightarrow 2x + 2\left ( 2 - x \right ) = 2x + 4 - 2x = 4$
$\Rightarrow C = \sqrt{4} = 2$
Vậy $C = 2\sqrt{x - 1}$ với $x \geq 2$
$C = 2$ với $x < 2$
