Question

tím các số nguyên x,y,z sao cho xy=-18,yz=48,zx=-24

Answer 1

xy . yz . zx = (-18).48.(-24)

x²y²z² = 20736

xyz = \(\sqrt{20736}\)= 144

=> z = \(\frac{xyz}{xy}=\frac{144}{-18}=-8\)

x = \(=\frac{xyz}{yz}=\frac{144}{48}=3\)

y = \(\frac{xyz}{xz}=\frac{144}{-24}=-6\)

vậy ...

Answer 2

                        Giải

Theo đề bài, ta có: \(\hept{\begin{cases}xy=-18\\yz=48\\zx=-24\end{cases}\Rightarrow\left(xy\right).\left(yz\right).\left(zx\right)=\left(-18\right).48.\left(-24\right)}\)

\(\Leftrightarrow x^2y^2z^2=20736\)

\(\Leftrightarrow\left(xyz\right)^2=20736\)

\(\Leftrightarrow xyz=\pm144\)

\(TH1:xyz=-144\)

\(\Rightarrow\hept{\begin{cases}z=-144\div\left(-18\right)=8\\x=-144\div48=-3\\y=-144\div\left(-24\right)=6\end{cases}}\)

\(TH2:xyz=144\)​

\(\Rightarrow\hept{\begin{cases}z=144\div\left(-18\right)=-8\\x=144\div48=3\\y=144\div\left(-24\right)=-6\end{cases}}\)