PTHĐGĐ là;
2x^2-2x-4=0
=>x^2-x-2=0
=>x=2 hoặc x=-1
=>y=8 hoặc y=2
=>A(2;8);B(-1;2); O(0;0)
\(OA=\sqrt{\left(0-2\right)^2+\left(0-8\right)^2}=2\sqrt{17}\)
\(OB=\sqrt{\left(-1\right)^2+2^2}=\sqrt{5}\)
\(AB=\sqrt{\left(-1-2\right)^2+\left(2-8\right)^2}=3\sqrt{5}\)
\(cosAOB=\dfrac{OA^2+OB^2-AB^2}{2\cdot OA\cdot OB}=\dfrac{7}{\sqrt{85}}\)
=>\(sinAOB=\dfrac{6}{\sqrt{85}}\)
\(S_{OAB}=\dfrac{1}{2}\cdot\dfrac{6}{\sqrt{85}}\cdot2\sqrt{17}\cdot\sqrt{5}=6\)
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