\(M\left(\dfrac{3}{2};\dfrac{3}{2}\right)\in\left(d\right)\Leftrightarrow3m+2n=3\)
\(\Leftrightarrow n=\dfrac{3\left(1-m\right)}{2}\left(1\right)\)
\(A\left(0;n\right)\in Oy;B\left(-\dfrac{n}{m};0\right)\in Ox\)
\(\Rightarrow OA=n;OB=\dfrac{n}{m}\)
\(S_{OAB}=\dfrac{1}{2}OA.OB=\dfrac{1}{2}n.\dfrac{n}{m}=\dfrac{n^2}{2m}\)
\(\Rightarrow S_{OAB}=\dfrac{\dfrac{9\left(1-m\right)^2}{4}}{2m}=\dfrac{m^2-2m+1}{8m}\left(do.\left(1\right)\right)\)
\(f\left(m\right)=\dfrac{m^2-2m+1}{8m}\left(m\ne0\right)\)
\(f'\left(m\right)=\dfrac{\left(2m-2\right)8m-8\left(m^2-2m+1\right)}{64m^2}=\dfrac{8m^2-8}{64m^2}\)
\(f'\left(m\right)=0\Leftrightarrow m=\pm1\)
Lập bảng biến thiên ta thấy \(f\left(m\right)_{min}=0\left(tại.m=1\right)\)
\(\left(1\right)\Rightarrow n=0\)
\(\Rightarrow3m-2n=3\)
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