Đáp án:
\(y = 19,16836496;z = 22,77890998\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
\dfrac{{10}}{{x - 5}} = \dfrac{6}{{y - 9}}\\
\dfrac{{10}}{{x - 5}} = \dfrac{{14}}{{z - 21}}\\
xyz = 6720
\end{array} \right.\\
\to \left\{ \begin{array}{l}
10y - 90 = 6x - 30\\
10z - 210 = 14x - 70\\
xyz = 6720
\end{array} \right.\\
\to \left\{ \begin{array}{l}
10y = 6x + 60\\
10z = 14x + 140\\
xyz = 6720
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{6x + 60}}{{10}}\\
z = \dfrac{{4x + 140}}{{10}}\\
x.\dfrac{{6x + 60}}{{10}}.\dfrac{{4x + 140}}{{10}} = 6720\left( * \right)
\end{array} \right.\\
\left( * \right) \to \dfrac{{\left( {6{x^2} + 60x} \right)\left( {4x + 140} \right)}}{{100}} = 6720\\
\to 24{x^3} + 840{x^2} + 240{x^2} + 8400 = 672000\\
\to 24{x^3} + 840{x^2} + 240{x^2} - 663600 = 0\\
\to x = 21,94727494\\
\to y = 19,16836496;z = 22,77890998
\end{array}\)
