Question

\(Bai1:\)Rút gọn\(P=\frac{\sqrt{a+4\sqrt{a-4}}+\sqrt{a-4\sqrt{a-4}}}{\sqrt{1-\frac{8}{a}+\frac{16}{a^2}}}\)

b) tim a \(\in Z\)(a>8) để P nguyên

Answer 1

\(P=\frac{\sqrt{\left(\sqrt{a-4}\right)^2+2.2.\sqrt{a-4}+4}+\sqrt{\left(\sqrt{a-4}\right)^2-2.2.\sqrt{a-4}+4}}{\sqrt{1^2-2.\frac{4}{a}}+\frac{4^2}{a^2}}\)

=\(\frac{\sqrt{\left(\sqrt{a-4}+2\right)^2}+\sqrt{\left(\sqrt{a-4}-2\right)^2}}{\sqrt{\left(1-\frac{4}{a}\right)^2}}\)

=\(\frac{|\sqrt{a-4}+2|+|\sqrt{a-4}-2|}{|1-\frac{4}{a}|}\)

=\(\frac{a-4+2+a-4-2}{1-\frac{4}{a}}\)

=\(\frac{2a-8}{\frac{a-4}{a}}\)

=\(\frac{2.\left(a-4\right)}{\frac{a-4}{a}}\)

=\(2.\left(a-4\right).\frac{a}{a-4}\)

=2a

(ĐKXĐ: a khác 4)