a, Ta có
\(2x^2=2x+4\Leftrightarrow2x^2-2x-4=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\\ \Rightarrow A\left(2;8\right);B\left(-1;2\right)\)
b, Ta có \(\Delta AOB\) vuông tại O
\(OA=\sqrt{2^2+8^2}=2\sqrt{17}\\ OB=\sqrt{\left(-1\right)^2+2^2}=\sqrt{5}\\ S_{\Delta AOB}=\dfrac{OA.OB}{2}=\dfrac{2\sqrt{17}.\sqrt{5}}{2}=\sqrt{85}\)