Example 7. Given $(x-y \sqrt{2})^{2}=6-4 \sqrt{2}$, find the values of the rational numbers $x, y$.

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Solve the original expression, which is transformed into

hence $\left\{\begin{array}{l}x^{2}+2 y^{2}=6, \\ 2 x y=4 .\end{array}\right.$
Solving it yields $\left\{\begin{array}{l}x_{1}=2, \\ y_{1}=1 ;\end{array},\left\{\begin{array}{l}x_{2}=-2, \\ y_{2}=-1\end{array}\right.\right.$.
Exercise 7. Given that $x, y$ are conjugate subnumbers, and
$(x+y)^{2}-3 x y i=4-6 i$, find the values of $x$, $y$.