Question

Tìm ba số x,y,z khác 0 biết: x^2.y.z=-4 ; x.y^2.z=2 ; x.y.z^2=-2

Answer 1

\(\left\{{}\begin{matrix}x,y,z\ne0\\x^2.y.z=-4\\xy^2z=2\\xyz^2=-2\end{matrix}\right.\)\(\begin{matrix}\left(1\right)\\\left(2\right)\\\left(3\right)\\\left(4\right)\end{matrix}\)

(2).(3).(4) \(\left(x^2yz\right).\left(xy^2z\right)\left(xyz^2\right)=\left(x^{2+1+1}.y^{1+2+1}.z^{1+1+2}\right)=\left(xyz\right)^4=\left(-4\right).2.\left(-2\right)=8\)\(\Leftrightarrow\left[{}\begin{matrix}xyz=2\\xyz=-2\end{matrix}\right.\)\(\begin{matrix}\left(I\right)\\\left(II\right)\end{matrix}\)

TH(I)

(2) => x =-2 ;(3) => y =1;(4) => z =-1

TH(II)

(2) => x =2 ; (3) => y =-1; (4) => z =1

(x;y;z)=(-2;1;-1);(2;-1;1)