Đáp án:

10

Giải thích các bước giải:

\(\begin{array}{*{20}{l}}
{C = 5{{\left( {\dfrac{{\sqrt {4 + 2\sqrt 3 } }}{{\sqrt 2 }} + \dfrac{{\sqrt {6 - 2\sqrt 5 } }}{{\sqrt 2 }} - \dfrac{{\sqrt 5 }}{{\sqrt 2 }}} \right)}^2} + {{\left( {\dfrac{{\sqrt {4 - 2\sqrt 3 } }}{{\sqrt 2 }} + \dfrac{{\sqrt {6 + 2\sqrt 5 } }}{{\sqrt 2 }} - \dfrac{{\sqrt 3 }}{{\sqrt 2 }}} \right)}^2}}\\
{ = 5{{\left( {\dfrac{{\sqrt {3 + 2\sqrt 3 .1 + 1} {\rm{ \;}} + \sqrt {5 - 2\sqrt 5 .1 + 1} {\rm{ \;}} - \sqrt 5 }}{{\sqrt 2 }}} \right)}^2} + \left( {\dfrac{{\sqrt {3 - 2\sqrt 3 .1 + 1} {\rm{ \;}} + \sqrt {5 + 2\sqrt 5 .1 + 1} {\rm{ \;}} - \sqrt 3 }}{{\sqrt 2 }}} \right)}\\
{ = 5.{{\left( {\dfrac{{\sqrt {{{\left( {\sqrt 3 {\rm{ \;}} + 1} \right)}^2}} {\rm{ \;}} + \sqrt {{{\left( {\sqrt 5 {\rm{ \;}} - 1} \right)}^2}} {\rm{ \;}} - \sqrt 5 }}{{\sqrt 2 }}} \right)}^2} + {{\left( {\dfrac{{\sqrt {{{\left( {\sqrt 3 {\rm{ \;}} - 1} \right)}^2}} {\rm{ \;}} + \sqrt {{{\left( {\sqrt 5 {\rm{ \;}} + 1} \right)}^2}} {\rm{ \;}} - \sqrt 3 }}{{\sqrt 2 }}} \right)}^2}}\\
{ = 5.{{\left( {\dfrac{{\sqrt 3 {\rm{ \;}} + 1 + \sqrt 5 {\rm{ \;}} - 1 - \sqrt 5 }}{{\sqrt 2 }}} \right)}^2} + {{\left( {\dfrac{{\sqrt 3 {\rm{ \;}} - 1 + \sqrt 5 {\rm{ \;}} + 1 - \sqrt 3 }}{{\sqrt 2 }}} \right)}^2}}\\
{ = 5.{{\left( {\dfrac{{\sqrt 3 }}{{\sqrt 2 }}} \right)}^2} + {{\left( {\dfrac{{\sqrt 5 }}{{\sqrt 2 }}} \right)}^2}}\\
{ = 5.\dfrac{3}{2} + \dfrac{5}{2} = \dfrac{{20}}{2} = 10}
\end{array}\)