2x=3y=4z
=>\(\dfrac{2x}{12}=\dfrac{3y}{12}=\dfrac{4z}{12}\)
=>\(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{3}\)
Đặt \(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{3}=k\)
=>x=6k; y=4k; z=3k
xyz=576
=>\(6k\cdot4k\cdot3k=576\)
=>\(72k^3=576\)
=>\(k^3=\dfrac{576}{72}=8=2^3\)
=>k=2
=>\(\left\{{}\begin{matrix}x=6\cdot2=12\\y=4\cdot2=8\\z=3\cdot2=6\end{matrix}\right.\)
=>Không có đáp án đúng
