Gọi \(A=\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
\(\Leftrightarrow\sqrt{2}A=\sqrt{2}.\sqrt{2+\sqrt{3}}-\sqrt{2}.\sqrt{2-\sqrt{3}}\)
\(=\sqrt{4+2.\sqrt{3}}-\sqrt{4-2.\sqrt{3}}\)
\(=\sqrt{1+2\sqrt{3}+3}-\sqrt{1-2\sqrt{3}+3}\)
\(=\sqrt{\left(1+\sqrt{3}\right)^2}-\sqrt{\left(1-\sqrt{3}\right)^2}\)
\(=1+\sqrt{3}-\left(\sqrt{3}-1\right)=2\)
\(\Rightarrow A=\frac{2}{\sqrt{2}}=\sqrt{2}\)
Đúng 0
Bình luận (0)
