Đáp án:
F=35
Giải thích các bước giải:
\(\begin{array}{l}
A = {\left[ {\sqrt 2 \left( {\sqrt 3 + 1} \right)\sqrt {2 - \sqrt 3 } - \sqrt {7 - 4\sqrt 3 } } \right]^2}\\
= {\left[ {\left( {\sqrt 3 + 1} \right)\sqrt {4 - 2\sqrt 3 } - \sqrt {7 - 4\sqrt 3 } } \right]^2}\\
= {\left[ {\left( {\sqrt 3 + 1} \right)\sqrt {3 - 2\sqrt 3 .1 + 1} - \sqrt {4 - 2.2\sqrt 3 + 3} } \right]^2}\\
= {\left[ {\left( {\sqrt 3 + 1} \right)\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} - \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} } \right]^2}\\
= {\left[ {\left( {\sqrt 3 + 1} \right)\left( {\sqrt 3 - 1} \right) - \left( {2 - \sqrt 3 } \right)} \right]^2}\\
= {\left( {3 - 1 - 2 + \sqrt 3 } \right)^2}\\
= 3\\
F = \left( {13 - 4\sqrt 3 } \right)\left( {7 + 4\sqrt 3 } \right) - 8\sqrt {20 + 2\sqrt {43 + 24\sqrt 3 } } \\
= \left( {13 - 4\sqrt 3 } \right)\left( {7 + 4\sqrt 3 } \right) - 8\sqrt {20 + 2\sqrt {{{\left( {3\sqrt 3 } \right)}^2} + 2.3\sqrt 3 .4 + 16} } \\
= \left( {13 - 4\sqrt 3 } \right)\left( {7 + 4\sqrt 3 } \right) - 8\sqrt {20 + 2\sqrt {{{\left( {3\sqrt 3 + 4} \right)}^2}} } \\
= \left( {91 + 52\sqrt 3 - 28\sqrt 3 - 48} \right) - 8\sqrt {20 + 2\left( {3\sqrt 3 + 4} \right)} \\
= \left( {43 + 24\sqrt 3 } \right) - 8\sqrt {28 + 6\sqrt 3 } \\
= \left( {43 + 24\sqrt 3 } \right) - 8\sqrt {{{\left( {3\sqrt 3 } \right)}^2} + 2.3\sqrt 3 .1 + 1} \\
= \left( {43 + 24\sqrt 3 } \right) - 8\sqrt {{{\left( {3\sqrt 3 + 1} \right)}^2}} \\
= \left( {43 + 24\sqrt 3 } \right) - 8\left( {3\sqrt 3 + 1} \right)\\
= 43 + 24\sqrt 3 - 24\sqrt 3 - 8 = 35
\end{array}\)
