Question

Tính

\(x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

Answer 1

x = \(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

x = \(\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}.3+3^2}\) - \(\sqrt{\left(2\sqrt{5}\right)^2-2.2\sqrt{5}.3+3^2}\)

x = \(\sqrt{\left(2\sqrt{5}+3\right)^2}\) - \(\sqrt{\left(2\sqrt{5}-3\right)^2}\)

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

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

x = \(2\sqrt{5}+3-2\sqrt{5}+3\) = 6

Answer 2

\(x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

\(\Rightarrow x=\sqrt{\left(3+2\sqrt{5}\right)^2}-\sqrt{\left(3-2\sqrt{5}\right)^2}\)

\(\Rightarrow x=3+2\sqrt{5}-\left(2\sqrt{5}-3\right)\)

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

\(\Rightarrow x=6\)

Answer 3

\(x=\sqrt{9+2.3.2\sqrt{5}+\left(2\sqrt{5}\right)^2}+\sqrt{9-2.3.2\sqrt{5}+\left(2\sqrt{5}\right)^2}\)

= \(\sqrt{\left(3+2\sqrt{5}\right)^2}+\sqrt{\left(3-2\sqrt{5}\right)2}\) = \(3+2\sqrt{5}+3-2\sqrt{5}\) = 6

=> x = 6

Answer 4

\(x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

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

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

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

\(=6\)