a) ĐK: \(a\ge4\)
\(P=\frac{\sqrt{a+4\sqrt{a-4}}+\sqrt{a-4\sqrt{a-4}}}{\sqrt{1-\frac{8}{a}+\frac{16}{a^2}}}\)
\(=\frac{\sqrt{\left(a-4\right)+4\sqrt{a-4}+4}+\sqrt{\left(a-4\right)-4\sqrt{a-4}+4}}{\sqrt{\left(1-\frac{4}{a}\right)^2}}\)
\(=\frac{\sqrt{\left(\sqrt{a-4}+2\right)^2}+\sqrt{\left(\sqrt{a-4}-2\right)^2}}{\left|1-\frac{4}{a}\right|}\)
\(=\frac{\sqrt{a-4}+2+\left|\sqrt{a-4}-2\right|}{1-\frac{4}{a}}\)
Nếu \(4\le a< 8\)thì: \(P=\frac{\sqrt{a-4}+2+2-\sqrt{a-4}}{1-\frac{4}{a}}=\frac{4}{\frac{a-4}{a}}=\frac{4a}{a-4}\)
Nếu \(a\ge8\)thì: \(P=\frac{\sqrt{a-4}+2+\sqrt{a-4}-2}{1-\frac{4}{a}}=\frac{2\sqrt{a-4}}{\frac{a-4}{a}}=\frac{2a\sqrt{a-4}}{a-4}\)
