\(\frac{x^2+2y^2}{300}=\frac{x^2-2y^2}{294}\)
\(\Leftrightarrow294\left(x^2+2y^2\right)=300\left(x^2-2y^2\right)\)
\(\Leftrightarrow294x^2+588y^2=300x^2-600y^2\)
\(\Leftrightarrow300x^2-294x^2=588y^2+600y^2\)
\(\Leftrightarrow6x^2=1188y^2\)
\(\Rightarrow\) \(\frac{x^2}{y^2}=\frac{1188}{6}=\frac{198}{1}\)
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