Đáp án:
B3:
b. \(\dfrac{{3\sqrt 2 + 5\sqrt 6 }}{4}\)
Giải thích các bước giải:
\(\begin{array}{l}
B3:\\
a.3\sqrt {ab} + 7.\sqrt {\dfrac{a}{b}} - 5\sqrt {\dfrac{b}{a}} - 3\sqrt {ab} \\
= \dfrac{{7.a - 5.b}}{{\sqrt {ab} }} = \dfrac{{7a - 5b}}{{\sqrt {ab} }}\\
b.\dfrac{{3\left( {\sqrt 5 + \sqrt 2 } \right)}}{{5 - 2}} + \dfrac{{\sqrt 6 - \sqrt 2 }}{{6 - 2}} + \dfrac{{\sqrt 6 - \sqrt 5 }}{{6 - 5}}\\
= \dfrac{{3\left( {\sqrt 5 + \sqrt 2 } \right)}}{3} + \dfrac{{\sqrt 6 - \sqrt 2 }}{4} + \dfrac{{\sqrt 6 - \sqrt 5 }}{1}\\
= \sqrt 5 + \sqrt 2 + \dfrac{{\sqrt 6 - \sqrt 2 }}{4} + \dfrac{{\sqrt 6 - \sqrt 5 }}{1}\\
= \dfrac{{4\sqrt 5 + 4\sqrt 2 + \sqrt 6 - \sqrt 2 + 4\sqrt 6 - 4\sqrt 5 }}{4}\\
= \dfrac{{3\sqrt 2 + 5\sqrt 6 }}{4}\\
B4:\\
M = 2x.\left| y \right|.4.\sqrt {xy} + 7.5.\left| {xy} \right|.\sqrt {xy} - 3.y.6.\left| x \right|\sqrt {xy} \left( {DK:x \ge 0;y \ge 0} \right)\\
= 8xy\sqrt {xy} + 35xy\sqrt {xy} - 18xy\sqrt {xy} \\
= 25xy\sqrt {xy} \\
M = \dfrac{{\sqrt y }}{{\sqrt x \left( {\sqrt y - \sqrt x } \right)}} - \dfrac{{\sqrt x }}{{\sqrt y \left( {\sqrt y - \sqrt x } \right)}}\left( {DK:x > 0;x > 0} \right)\\
= \dfrac{{y - x}}{{\sqrt {xy} \left( {\sqrt y - \sqrt x } \right)}}\\
= \dfrac{{\left( {\sqrt y - \sqrt x } \right)\left( {\sqrt y + \sqrt x } \right)}}{{\sqrt {xy} \left( {\sqrt y - \sqrt x } \right)}}\\
= \dfrac{{\sqrt y + \sqrt x }}{{\sqrt {xy} }}
\end{array}\)
