Question

Phân tích đa thức thành nhân tử:

a) \(\frac{\sqrt{9+2\sqrt{2}+2\sqrt{3}+2\sqrt{2}.\sqrt{3}}}{6+3\sqrt{2}+3\sqrt{3}}\)

b) A = \(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)

Answer 1

b) Ta có: \(A=\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)

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

\(=\frac{\sqrt{5-2\cdot\sqrt{5}\cdot1+1}-\sqrt{5+2\cdot\sqrt{5}\cdot1+1}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}-\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}\)

\(=\frac{\left|\sqrt{5}-1\right|-\left|\sqrt{5}+1\right|}{\sqrt{2}}\)

\(=\frac{\sqrt{5}-1-\left(\sqrt{5}+1\right)}{\sqrt{2}}\)(Vì \(\sqrt{5}>1>0\))

\(=\frac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}\)

\(=-\frac{2}{\sqrt{2}}=-\sqrt{2}\)

Answer 2

còn câu a ạ?? :<