Question

bài 2 : rút gọn g, \(\sqrt{3-\sqrt{2}}-\sqrt{3+\sqrt{2}}\)

Answer 1

Gọi \(\sqrt{3-\sqrt{2}}-\sqrt{3+\sqrt{2}}\) là M

Ta có: \(M=\sqrt{3-\sqrt{2}}-\sqrt{3+\sqrt{2}}\)

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

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

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

\(=3-\sqrt{2}-2\sqrt{7}+3+\sqrt{2}\)

\(=6-2\sqrt{7}\)

=> M = \(\sqrt{6-2\sqrt{7}}\)

Vì M âm nên: M = \(-\sqrt{6-2\sqrt{7}}\)