Question

[Nguyễn Hương Giang]

Giải giúp mình nhé
\(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)

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

Answer 1

[Aoi Ogata]

\(\left(1+\sqrt{3}-\sqrt{2}\right)\left(1+\sqrt{3}+\sqrt{2}\right)\)

\(=\left(1+\sqrt{3}\right)^2-2\)

\(=3+2\sqrt{3}+1-2\)

\(=2\sqrt{3}+2\)

\(=2\left(\sqrt{3}+1\right)\)

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

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

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

\(=6+6-2\sqrt{5}\)

\(=12-2\sqrt{5}\)

\(=2\left(6-\sqrt{5}\right)\)

Answer 2

[Nguyễn Hương Giang]

Cảm ơn bạn nhiều nhé.