Question

Cho \(A=\dfrac{\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}}{\sqrt{1-\dfrac{8}{x}+\dfrac{16}{x^2}}}\)

a) Rút gọn A

Answer 1

\(A=\dfrac{\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}}{\sqrt{1-\dfrac{8}{x}+\dfrac{16}{x^2}}}\)

\(=\dfrac{\sqrt{\left(x-4\right)+4\sqrt{x-4}+4}+\sqrt{\left(x-4\right)-4\sqrt{x-4}+4}}{\sqrt{\left(\dfrac{4}{x}-1\right)^2}}\)

\(=\dfrac{\sqrt{\left(\sqrt{x-4}+2\right)}^2+\sqrt{\left(\sqrt{x-4}-2\right)}^2}{\left|\dfrac{4}{x}-1\right|}\)

\(=\dfrac{\left|\sqrt{x-4}+2\right|+\left|\sqrt{x-4}-2\right|}{\left|\dfrac{4}{x}-1\right|}\)