$\begin{array}{l} \dfrac{{\sqrt {\sqrt 5 + 2} + \sqrt {\sqrt 5 - 2} }}{{\sqrt {\sqrt 5 + 1} }}\\ \Rightarrow {\left( {\sqrt {\sqrt 5 + 2} + \sqrt {\sqrt 5 - 2} } \right)^2} = 2\sqrt 5 + 2\sqrt {5 - 4} = 2\sqrt 5 + 2\\ \Rightarrow \sqrt {\sqrt 5 + 2} + \sqrt {\sqrt 5 - 2} = \sqrt 2 \left( {\sqrt {\sqrt 5 + 1} } \right)\\ \Rightarrow \dfrac{{\sqrt {\sqrt 5 + 2} + \sqrt {\sqrt 5 - 2} }}{{\sqrt {\sqrt 5 + 1} }} = \dfrac{{\sqrt 2 \left( {\sqrt {\sqrt 5 + 1} } \right)}}{{\sqrt {\sqrt 5 + 1} }} = \sqrt 2 \\ \Rightarrow \dfrac{{\sqrt {\sqrt 5 + 2} + \sqrt {\sqrt 5 - 2} }}{{\sqrt {\sqrt 5 + 1} }} - \sqrt {3 - 2\sqrt 2 } = \sqrt 2 - \sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} \\ = 1\\ \Rightarrow A = {x^{2012}} + 2{x^{2013}} + 3{x^2}^{^{2014}} = 1 + {2.1^{2013}} + {3.1^{{2^{2014}}}} = 6\\ \end{array}$
