Question

bài 2 : rút gọn b,\(\left(\sqrt{3+\sqrt{5}-}\sqrt{3-\sqrt{5}}\right)^2\)

Answer 1

\(\left(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\right)^2=3+\sqrt{5}+3-\sqrt{5}-2\sqrt{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}=3+\sqrt{5}+3-\sqrt{5}-4=2\)

Answer 2

Giải:

\(\left(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\right)^2\)

\(=\left(\sqrt{3+\sqrt{5}}\right)^2-2\sqrt{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}+\left(\sqrt{3-\sqrt{5}}\right)^2\)

\(=\left|3+\sqrt{5}\right|-2\sqrt{9-5}+\left|3-\sqrt{5}\right|\)

\(=3+\sqrt{5}-2\sqrt{4}+3-\sqrt{5}\)

\(=3+\sqrt{5}-4+3-\sqrt{5}\)

\(=2\)

Vậy ...