Đáp án:
\(E = \sqrt 3 \)
Giải thích các bước giải:
\(\begin{array}{l}
a.A = \sqrt 3 - \dfrac{{2\sqrt 3 }}{{\sqrt 3 + 1}} = \dfrac{{3 + \sqrt 3 - 2\sqrt 3 }}{{\sqrt 3 + 1}}\\
= \dfrac{{3 - \sqrt 3 }}{{\sqrt 3 + 1}} = - 3 + 2\sqrt 3 \\
b.B = \sqrt 3 + 2 + \dfrac{{\sqrt 2 \left( {1 + \sqrt 2 } \right)}}{{1 + \sqrt 2 }} - \dfrac{{2 + \sqrt 3 }}{{4 - 3}}\\
= \sqrt 3 + 2 + \sqrt 2 - 2 - \sqrt 3 \\
= \sqrt 2 \\
c.C = - \dfrac{{6\left( {\sqrt 5 - \sqrt 3 } \right)}}{{5 - 3}} - \dfrac{{4\left( {2 - \sqrt 5 } \right)}}{{4 - 5}} + 3\sqrt 3 \\
= - \dfrac{{6\sqrt 5 - 6\sqrt 3 }}{2} + 8 - 4\sqrt 5 + 3\sqrt 3 \\
= \dfrac{{ - 6\sqrt 5 + 6\sqrt 3 + 16 - 8\sqrt 5 + 6\sqrt 3 }}{2}\\
= \dfrac{{ - 14\sqrt 5 + 12\sqrt 3 + 16}}{2}\\
= - 7\sqrt 5 + 6\sqrt 3 + 8\\
d.D = \dfrac{{7 + 2\sqrt {35} + 5 + 7 - 2\sqrt {35} + 5}}{{7 - 5}}\\
= \dfrac{{24}}{2} = 12\\
e.E = \left[ {\dfrac{{\sqrt 5 + 2}}{{5 - 4}} - \dfrac{{2\sqrt 5 - 2\sqrt 3 }}{{5 - 3}}} \right].\sqrt {{{\left( {2\sqrt 3 } \right)}^2} - 2.2\sqrt 3 .3 + 9} \\
= \left( {\sqrt 5 + 2 - \dfrac{{2\sqrt 5 - 2\sqrt 3 }}{2}} \right).\sqrt {{{\left( {2\sqrt 3 - 3} \right)}^2}} \\
= \left( {\sqrt 5 + 2 - \sqrt 5 + \sqrt 3 } \right).\left( {2\sqrt 3 - 3} \right)\\
= \left( {2 + \sqrt 3 } \right).\left( {2\sqrt 3 - 3} \right)\\
= 4\sqrt 3 - 6 + 6 - 3\sqrt 3 \\
= \sqrt 3
\end{array}\)
