\(\Rightarrow\frac{x^8}{256}=\frac{y^8}{65536}=\frac{x^4.y^4}{4096}=\frac{16}{4096}=\frac{1}{256}\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=1\\x=-1\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}y=2\\y=-2\end{array}\right.\)
Mà 2 và 4 cùng dấu
=> x; y cùng dấu
\(\Rightarrow\left(x;y\right)\in\left\{\left(1;2\right);\left(-1;-2\right)\right\}\)
=>\(\frac{x}{2}=\frac{y}{4}=>\frac{x^4}{16}=\frac{y^4}{256}=\frac{x^4.y^4}{16.256}=\frac{16}{4096}=\frac{1}{256}\)
=>\(\begin{cases}x=1\\x=-1\end{cases}\)
=>\(\begin{cases}y=2\\y=-2\end{cases}\)
vậy:
\(x=1;y=2\)
\(x=-1;y=-2\)
\(\frac{x}{2}=\frac{y}{4}\) => \(\frac{x^4}{2^4}=\frac{y^4}{4^4}=\left(\frac{x}{2}\right)^4=\left(\frac{y}{4}\right)^4\)
Đặt: \(\left(\frac{x}{2}\right)^4=\left(\frac{y}{4}\right)^4=k\)
=> \(x^4=k.2^4\)
\(y^4=k.4^4\)
\(\left(xy\right)^4=8^4.k^2=4096.k^2=16\) => \(k^2=\frac{1}{256}\)
=> \(k=\frac{\sqrt{1}}{\sqrt{256}}=\frac{1}{16}\)
=> \(x=\sqrt[4]{\frac{1}{16}.2^4}=1\)
\(y=\sqrt[4]{\frac{1}{16}.4^4}=2\)