Question

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

Answer 1

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

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

\(=\left(2-\sqrt{3}\right)+2.1.1+\left(2+\sqrt{3}\right)\)

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

\(=6\)

\(\Rightarrow A=\sqrt{6}\)

Answer 2

\(\sqrt{\left(2-\sqrt{3}\right)^2\left(2+\sqrt{3}\right)}+\sqrt{\left(2+\sqrt{3}\right)^2\left(2-\sqrt{3}\right)}\)
=\(\sqrt{\left(4-3\right)\left(2-\sqrt{3}\right)}+\sqrt{\left(4-3\right)\left(2+\sqrt{3}\right)}\)
=\(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
Đặt P²=(\(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\))<sup>2
=\(2-\sqrt{3}\) + 2\(\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}\)+\(2+\sqrt{3}\)
=2+2\(\sqrt{1}\)+2=6

tick nha</sup>