Gọi \(A\left(x_A;y_A\right);B\left(x_B;y_B\right)\) la tọa độ của 2 đồ thị hàm số
Ta có : \(\left(P\right)=\left(d\right)\)
\(\Leftrightarrow\dfrac{x^2}{2}=\dfrac{-x+3}{2}\)
\(\Leftrightarrow\dfrac{x^2+x-3}{2}=0\)
\(\Leftrightarrow x^2+x-3=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1=\dfrac{-1+\sqrt{13}}{2}\\x_2=\dfrac{-1-\sqrt{13}}{2}\end{matrix}\right.\)
Thay \(x_1=\dfrac{-1+\sqrt{13}}{2}\) vào \(\left(P\right):y=\dfrac{x^2}{2}\Rightarrow y=\dfrac{-1+\sqrt{13}}{2}:2=\dfrac{-1+\sqrt{13}}{4}\)
Thay \(x_2=\dfrac{-1-\sqrt{13}}{2}\) vào \(\left(d\right):y=\dfrac{-x+3}{2}\Rightarrow y=[-\left(\dfrac{-1-\sqrt{13}}{2}\right)+3]:2=\dfrac{-5+\sqrt{13}}{4}\)
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