Đáp án:
\[B = - 2\sqrt 3 \]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
B = \frac{{a\sqrt a + b\sqrt b }}{{a - b}} - \frac{{\sqrt {ab} }}{{\sqrt a - \sqrt b }}\\
= \frac{{\left( {\sqrt a + \sqrt b } \right)\left( {a - \sqrt {ab} + b} \right)}}{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a - \sqrt b } \right)}} - \frac{{\sqrt {ab} }}{{\sqrt a - \sqrt b }}\\
= \frac{{a - \sqrt {ab} + b}}{{\sqrt a - \sqrt b }} - \frac{{\sqrt {ab} }}{{\sqrt a - \sqrt b }}\\
= \frac{{a - 2\sqrt {ab} + b}}{{\sqrt a - \sqrt b }}\\
= \frac{{{{\left( {\sqrt a - \sqrt b } \right)}^2}}}{{\sqrt a - \sqrt b }} = \sqrt a - \sqrt b \\
a = \frac{1}{{7 + 4\sqrt 3 }} \Rightarrow \sqrt a = \frac{1}{{\sqrt {7 + 4\sqrt 3 } }} = \frac{1}{{\sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} }} = \frac{1}{{2 + \sqrt 3 }}\\
b = \frac{1}{{7 - 4\sqrt 3 }} \Rightarrow \sqrt b = \frac{1}{{\sqrt {7 - 4\sqrt 3 } }} = \frac{1}{{\sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} }} = \frac{1}{{2 - \sqrt 3 }}\\
\Rightarrow B = \sqrt a - \sqrt b = \frac{1}{{2 + \sqrt 3 }} - \frac{1}{{2 - \sqrt 3 }} = \frac{{2 - \sqrt 3 - 2 - \sqrt 3 }}{{\left( {2 - \sqrt 3 } \right)\left( {2 + \sqrt 3 } \right)}} = - 2\sqrt 3
\end{array}\)
