Question

[nmixx aespa]

RÚT GỌN BIỂU THỨC

\(\dfrac{2-\sqrt{5}}{2+\sqrt{5}}+\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)

Answer 1

[HT.Phong (9A5)]

\(\dfrac{2-\sqrt{5}}{2+\sqrt{5}}+\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)

\(=\dfrac{\left(2-\sqrt{5}\right)^2}{\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)}+\dfrac{\left(\sqrt{5}+2\right)^2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}\)

\(=\dfrac{4-4\sqrt{5}+5}{4-5}+\dfrac{5+4\sqrt{5}+4}{5-4}\)

\(=-4+4\sqrt{5}-5+5+4\sqrt{5}+4\)

\(=8\sqrt{5}\)

Answer 2

[Nguyễn Lê Phước Thịnh]

\(=\dfrac{\left(2-\sqrt{5}\right)\left(2-\sqrt{5}\right)}{\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)}+\dfrac{\left(\sqrt{5}+2\right)^2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}\)

\(=\dfrac{9-4\sqrt{5}}{-1}+9+4\sqrt{5}\)

=9+4căn 5-9+4căn 5

=8*căn 5