Question

Tìm x.y.z biết:

a, xy=2/7;yz=3/2;zx=3/7

b, xy=9z;yz=4x; zx=16y

Answer 1

Theo bài ra ta có: \(xy=\dfrac{2}{7}\left(1\right)\)

\(yz=\dfrac{3}{2}\left(2\right)\)

\(zx=\dfrac{3}{7}\left(3\right)\)

Vế nhân vế (1);(2);(3), ta có: \(xy.yz.zx=\dfrac{2}{7}.\dfrac{3}{2}.\dfrac{3}{7}\)

\(\left(x.y.z\right)^2=\dfrac{9}{49}=\left(\dfrac{3}{7}\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}xyz=\dfrac{3}{7}\\xyz=-\dfrac{3}{7}\end{matrix}\right.\)

b, Theo bài ra ta có: \(xy=9z;yz=4x;zx=16y\)

Nhân vế theo vế ta có: \(\left(xyz\right)^2=xyz.576\)

\(\Rightarrow xyz=576\)