Question

tìm x,y biết:2x+3y=0 và xy=-54

 

 

Answer 1

\(2x+3y=0\)

\(\Leftrightarrow2x=-3y\)

\(\Rightarrow\frac{x}{-3}=\frac{y}{2}\Rightarrow\frac{-x}{3}=\frac{y}{2}\)

Ta có : \(\left(\frac{-x}{3}\right)^2=\frac{-x}{3}\cdot\frac{-x}{3}=\frac{-x}{3}\cdot\frac{y}{2}=\frac{-xy}{3\cdot2}=\frac{54}{6}=9\)

\(\Rightarrow\left(\frac{-x}{3}\right)=\left(\pm3\right)^2\)

\(\Rightarrow\orbr{\begin{cases}\frac{-x}{3}=\frac{y}{2}=-3\\\frac{-x}{3}=\frac{y}{2}=3\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=9;y=-6\\x=-9;y=6\end{cases}}\)

Vậy ......