a) Thay $x = 5$ vào $A$ ta được:
$A(5) = \sqrt{5 - 2\sqrt{5 - 1}} + \sqrt{5 + 2\sqrt{5 - 1}}$
$ = \sqrt{5 - 2\sqrt{4}} + \sqrt{5 + 2\sqrt{4}}$
$ = \sqrt{5 - 2.2} + \sqrt{5 + 2.2}$
$ = \sqrt{1} + \sqrt{9}$
$ = 1 + 3 = 4$
b) Ta có:
$A = \sqrt{x - 2\sqrt{x -1}} + \sqrt{x + 2\sqrt{x - 1}}$
$\Leftrightarrow A^{2} = x - 2\sqrt{x-1} + x + 2\sqrt{x -1} + 2.\sqrt{(x - 2\sqrt{x-1})(x + 2\sqrt{x - 1})}$
$ = 2x + 2\sqrt{x^{2} - 4(x - 1)}$
$ = 2x + 2\sqrt{(x - 2)^{2}}$
$ = 2x + 2.|x - 2|$
$ = 2x + 2(2 - x)$ (do $x \leq 2$)
$ = 4$
$\Rightarrow A = \sqrt{4} = 2$
