M thuộc trục tung nên M(0;y)
\(\overrightarrow{AM}=\left(2;y-2\right)\)
\(\overrightarrow{AB}=\left(3;-2\right)\)
\(\widehat{MAB}=45^0\)
\(\Leftrightarrow\dfrac{2\cdot3+\left(y-2\right)\cdot\left(-2\right)}{\sqrt{2^2+\left(y-2\right)^2}\cdot\sqrt{3^2+2^2}}=\dfrac{\sqrt{2}}{2}\)
=>\(\dfrac{6-2y+4}{\sqrt{13\left(4+y^2-4y+4\right)}}=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\dfrac{10-2y}{\sqrt{13\left(y^2-4y+8\right)}}=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\sqrt{26\left(y^2-4y+8\right)}=20-4y\)
=>\(\left\{{}\begin{matrix}y< =5\\26\left(y^2-4y+8\right)=\left(20-4y\right)^2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y< =5\\16y^2-160y+400-26y^2+104y-204=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y< =5\\-10y^2-56y+196=0\end{matrix}\right.\Leftrightarrow y=\dfrac{-14\pm7\sqrt{14}}{5}\)
