a/ \(x\le8\)
\(\Leftrightarrow x^2+x+12=\left(8-x\right)^2\)
\(\Leftrightarrow x^2+x+12=x^2-16x+64\)
\(\Leftrightarrow17x=52\Rightarrow x=\frac{52}{17}\)
b/ \(x\le4\)
\(\Leftrightarrow x^2+3x-1=\left(4-x\right)^2\)
\(\Leftrightarrow x^2+3x-1=x^2-8x+16\)
\(\Leftrightarrow11x=17\Rightarrow x=\frac{17}{11}\)
c/ \(\left\{{}\begin{matrix}x^2-3x\ge0\\2x-1\ge0\end{matrix}\right.\) \(\Rightarrow x\ge3\)
\(x^2-3x=2x-1\)
\(\Leftrightarrow x^2-5x+1=0\Rightarrow\left[{}\begin{matrix}x=\frac{5+\sqrt{21}}{2}\\x=\frac{5-\sqrt{21}}{2}\left(l\right)\end{matrix}\right.\)
d/ \(2-x\ge0\Rightarrow x\le2\)
\(x^2+2x+4=2-x\)
\(\Leftrightarrow x^2+3x+2=0\Rightarrow\left[{}\begin{matrix}x=-1\\x=-2\end{matrix}\right.\)
e/ \(2x^2-x\ge0\Rightarrow\left[{}\begin{matrix}x\le0\\x\ge\frac{1}{2}\end{matrix}\right.\)
\(x^2+2x+4=2x^2-x\)
\(\Leftrightarrow x^2-3x-4=0\Rightarrow\left[{}\begin{matrix}x=-1\\x=4\end{matrix}\right.\)
f/ \(x\ge2\)
\(2x-1=\left(x-2\right)^2\)
\(\Leftrightarrow x^2-6x+5=0\Rightarrow\left[{}\begin{matrix}x=1\left(l\right)\\x=5\end{matrix}\right.\)
