Question

Rút gọn :

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

Answer 1

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

B=\(\sqrt{\frac{1}{2}\left(6+2\sqrt{5}\right)}\)-\(\sqrt{\frac{1}{2}\left(6-2\sqrt{5}\right)}\)-\(\sqrt{2}\)

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

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

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

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

B=\(\sqrt{2}\)-\(\sqrt{2}\)=0

Answer 2

Ta có :

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

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

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

\(=\sqrt{5}+1-\left|\sqrt{5}-1\right|-2=0\)

\(\Rightarrow B=0\)

Answer 3

Ta có :

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

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

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

\(B=\sqrt{5}+1-\left(\sqrt{5}-1\right)-2=0\)

\(B=0\)