\(\Delta=1+4.3.5=61\)
Pt có 2 nghiệm pb: \(\left\{{}\begin{matrix}x_1=\frac{-1+\sqrt{61}}{6}\\x_2=\frac{-1-\sqrt{61}}{6}\end{matrix}\right.\)
b/ \(\left\{{}\begin{matrix}x-1\ge0\\2x+4=\left(x-1\right)^2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x^2-4x-3=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\ge1\\\left[{}\begin{matrix}x=2+\sqrt{7}\\x=2-\sqrt{7}< 1\left(l\right)\end{matrix}\right.\end{matrix}\right.\)
c/ ĐKXĐ: ...
\(\Leftrightarrow\left\{{}\begin{matrix}y^2-3xy=4\\x^2+y^2=4xy+1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y^2-3xy=4\\4x^2+4y^2-16xy=4\end{matrix}\right.\)
\(\Rightarrow4x^2+3y^2-13xy=0\) \(\Leftrightarrow\left(4x-y\right)\left(x-3y\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}y=4x\\x=3y\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left(4x\right)^2-3x.4x=4\\y^2-3.3y.y=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}4x^2=4\\-8y^2=4\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\Rightarrow y=4\\x=-1\Rightarrow y=-4\end{matrix}\right.\)
