i) \(\Leftrightarrow\left(2x-3\right)^2+\left(y-4\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\y-4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=4\end{matrix}\right.\)
j) \(\Leftrightarrow\left(2y+3\right)^2+\left(x+4\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2y+3=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{3}{2}\\x=-4\end{matrix}\right.\)
\(i.4x^2+25-12x-8y+y^2=0\\ \Rightarrow4x^2-12x+9+y^2-8y+16=0\\ \Rightarrow\left(2x-3\right)^2+\left(y-4\right)^2=0\\ \Rightarrow\left[{}\begin{matrix}2x-3=0\\y-4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=3\\y=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\y=4\end{matrix}\right.\)
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\(j.4y^2+12y+25+8x+x^2=0\\ \Rightarrow4y^2+12y+9+x^2+8x+16=0\\ \Rightarrow\left(2y+3\right)^2+\left(x+4\right)^2=0\\ \Rightarrow\left[{}\begin{matrix}2y+3=0\\x+4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2y=-3\\x=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}y=\dfrac{-3}{2}\\x=-4\end{matrix}\right.\)
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