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
\(x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
\(\Rightarrow x=\sqrt{\left(3+2\sqrt{5}\right)^2}-\sqrt{\left(3-2\sqrt{5}\right)^2}\)
\(\Rightarrow x=3+2\sqrt{5}-\left(2\sqrt{5}-3\right)\)
\(\Rightarrow x=3+2\sqrt{5}-2\sqrt{5}+3\)
\(\Rightarrow x=6\)
\(x=\sqrt{9+2.3.2\sqrt{5}+\left(2\sqrt{5}\right)^2}+\sqrt{9-2.3.2\sqrt{5}+\left(2\sqrt{5}\right)^2}\)
= \(\sqrt{\left(3+2\sqrt{5}\right)^2}+\sqrt{\left(3-2\sqrt{5}\right)2}\) = \(3+2\sqrt{5}+3-2\sqrt{5}\) = 6
=> x = 6
\(x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
\(=\sqrt{\left(3+2\sqrt{5}\right)^2}-\sqrt{\left(3-2\sqrt{5}\right)^2}\)
\(=3+2\sqrt{5}-\left(2\sqrt{5}-3\right)\)
\(=3+2\sqrt{5}-2\sqrt{5}+3\)
\(=6\)
