a) \(\left(2x-3\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(2x-3-x+1\right)\left(2x-3+x-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\3x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\3x=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)
b) \(\left(4x-5\right)^2-2\left(4x+3\right)-3=0\)
\(\Leftrightarrow16x^2-40x+25-8x-6-3=0\)
\(\Leftrightarrow16x^2-48x+16=0\)
\(\Leftrightarrow16\left(x^2-3x+1\right)=0\)
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c) \(x^2+y^2-6x+10y+34=0\)
\(\Leftrightarrow\left(x^2-6x+9\right)+\left(y^2+10y+25\right)=0\)
\(\Leftrightarrow\left(x-3\right)^2+\left(y+5\right)^2=0\)
Mà: \(\left\{{}\begin{matrix}\left(x-3\right)^2\ge0\\\left(y+5\right)^2\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\y+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-5\end{matrix}\right.\)
d) \(9x^2+4y^2-12x+4y+5=0\)
\(\Leftrightarrow\left(9x^2-12x+4\right)+\left(4y^2+4y+1\right)=0\)
\(\Leftrightarrow\left(3x-2\right)^2+\left(2y+1\right)^2=0\)
Mà: \(\left\{{}\begin{matrix}\left(3x-2\right)^2\ge0\\\left(2y+1\right)^2\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-2=0\\2y+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=2\\2y=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=-\dfrac{1}{2}\end{matrix}\right.\)
e) \(2x^2+y^2-2xy+8x+16=0\)
\(\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(x^2+8x+16\right)=0\)
\(\Leftrightarrow\left(x-y\right)^2+\left(x+4\right)^2=0\)
Mà: \(\left\{{}\begin{matrix}\left(x-y\right)^2\ge0\\\left(x+4\right)^2\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=y\\x=-4\end{matrix}\right.\)
\(\Leftrightarrow x=y=-4\)