Đáp án:
\(2)C = 4\sqrt 2 \)
Giải thích các bước giải:
\(\begin{array}{l}
1)A = \dfrac{{2\left( {\sqrt 5 + \sqrt 3 } \right)}}{{5 - 3}} + \dfrac{{3\left( {\sqrt 6 - \sqrt 3 } \right)}}{{6 - 3}}\\
= \dfrac{{2\left( {\sqrt 5 + \sqrt 3 } \right)}}{2} + \dfrac{{3\left( {\sqrt 6 - \sqrt 3 } \right)}}{3}\\
= \sqrt 5 + \sqrt 3 + \sqrt 6 - \sqrt 3 = \sqrt 5 + \sqrt 6 \\
B = \dfrac{1}{{1 + \sqrt 2 + \sqrt 3 }} = \dfrac{{\left( {1 + \sqrt 2 } \right) - \sqrt 3 }}{{{{\left( {1 + \sqrt 2 } \right)}^2} - 3}}\\
= \dfrac{{1 + \sqrt 2 - \sqrt 3 }}{{3 + 2\sqrt 2 - 3}}\\
= \dfrac{{1 + \sqrt 2 - \sqrt 3 }}{{2\sqrt 2 }}\\
2)A = \sqrt {4 - 2.2.\sqrt 3 + 3} - \sqrt {4 + 2.2.\sqrt 3 + 3} \\
= \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} \\
= 2 - \sqrt 3 - 2 - \sqrt 3 \\
= - 2\sqrt 3 \\
B = \sqrt {4 + \sqrt 7 } - \sqrt {4 - \sqrt 7 } \\
= \dfrac{{\sqrt {8 + 2\sqrt 7 } - \sqrt {8 - 2\sqrt 7 } }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {7 + 2\sqrt 7 .1 + 1} - \sqrt {7 - 2\sqrt 7 .1 + 1} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 7 + 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 7 - 1} \right)}^2}} }}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 7 + 1 - \sqrt 7 + 1}}{{\sqrt 2 }}\\
= \dfrac{2}{{\sqrt 2 }} = \sqrt 2 \\
C = \sqrt {2 + \sqrt 3 } + \sqrt {14 - 5\sqrt 3 } + \sqrt 2 \\
= \dfrac{{\sqrt {4 + 2\sqrt 3 } + \sqrt {28 - 10\sqrt 3 } + 2}}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {3 + 2\sqrt 3 .1 + 1} + \sqrt {25 - 2.5.\sqrt 3 + 3} + 2}}{{\sqrt 2 }}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} + \sqrt {{{\left( {5 - \sqrt 3 } \right)}^2}} + 2}}{{\sqrt 2 }}\\
= \dfrac{{\sqrt 3 + 1 + 5 - \sqrt 3 + 2}}{{\sqrt 2 }}\\
= \dfrac{8}{{\sqrt 2 }} = 4\sqrt 2
\end{array}\)
