Đáp án:
\(\Rightarrow\left[{}\begin{matrix}x=-1\\y=-2\end{matrix}\right.\)
Giải thích các bước giải:
\(x^4.y^4=\left(x.y\right)^4=16\Leftrightarrow x.y=2\)
\(\dfrac{x}{2}=\dfrac{y}{4}=k\)
\(\Rightarrow\dfrac{x}{2}=k\Leftrightarrow x=2k\)
\(\Rightarrow\dfrac{y}{4}=k\Leftrightarrow y=4k\)
Mà \(x.y=2\)
`=>` ta có :
\(2k.4k=2\)
\(\Leftrightarrow8k^2=2\Leftrightarrow k^2=\dfrac{1}{4}\Leftrightarrow\left[{}\begin{matrix}k=\dfrac{1}{2}\\k=-\dfrac{1}{2}\end{matrix}\right.\)
`+) TH1: Khi` \(k=\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)
`+ ) TH2 : Khi` \(k=-\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\y=-2\end{matrix}\right.\)
