Tính giá trị biểu thức \(P = \frac{{{{\left( {4 + 2\sqrt 3 } \right)}^{2018}}.

* Hướng dẫn giải

Ta có: \(P = \frac{{{{\left( {4 + 2\sqrt 3 } \right)}^{2018}}.{{\left( {1 - \sqrt 3 } \right)}^{2017}}}}{{{{\left( {1 + \sqrt 3 } \right)}^{2019}}}} = \frac{{{{\left( {{{\left( {\sqrt 3  + 1} \right)}^2}} \right)}^{2018}}.{{\left( {1 - \sqrt 3 } \right)}^{2017}}}}{{{{\left( {1 + \sqrt 3 } \right)}^{2019}}}} = \frac{{{{\left( {\sqrt 3  + 1} \right)}^{4036}}.{{\left( {1 - \sqrt 3 } \right)}^{2017}}}}{{{{\left( {1 + \sqrt 3 } \right)}^{2019}}}}\)

\( = {\left( {\sqrt 3  + 1} \right)^{2017}}.{\left( {1 - \sqrt 3 } \right)^{2017}} = {\left[ {\left( {\sqrt 3  + 1} \right)\left( {1 - \sqrt 3 } \right)} \right]^{2017}} = {\left( { - 2} \right)^{2017}} =  - {2^{2017}}\)