Đáp án:
$B= \dfrac{{26}}{{25}}$
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{3x - 2y}}{2} = \dfrac{{2z - 4x}}{3} = \dfrac{{4y - 3z}}{2}\\
\Rightarrow \dfrac{{2z - 4x}}{3} = \dfrac{{6x - 4y}}{4} = \dfrac{{4y - 3z}}{2}\\
= \dfrac{{6x - 4y + 4y - 3z}}{6} = \dfrac{{2z - 4x}}{3}\\
\Rightarrow \dfrac{{2x - z}}{2} = \dfrac{{2z - 4x}}{3}\\
\Rightarrow 6x - 3z = 4z - 8x \Rightarrow z = 2x\\
+ )\,\dfrac{{3x - 2y}}{2} = \dfrac{{6z - 12x}}{9} = \dfrac{{8y - 6z}}{4}\\
= \dfrac{{6z - 12x + 8y - 6z}}{{13}}\\
\Rightarrow \dfrac{{3x - 2y}}{2} = \dfrac{{ - 12x + 8y}}{{13}}\\
\Rightarrow 39x - 26y = - 24x + 16y\\
\Leftrightarrow 63x = 42y \Rightarrow y = \dfrac{3}{2}x\\
\Rightarrow B = \dfrac{{x.\dfrac{3}{2}x + \dfrac{3}{2}x.2x + 2x.x}}{{{x^2} + {{\left( {\dfrac{3}{2}x} \right)}^2} + {{\left( {2x} \right)}^2}}}\\
= \dfrac{{\dfrac{{13}}{2}{x^2}}}{{\dfrac{{25}}{4}{x^2}}} = \dfrac{{26}}{{25}}
\end{array}\)
