\(d\left(O;d\right)=\dfrac{\left|\left(m-2\right)\cdot0+\left(m-1\right)\cdot0-1\right|}{\sqrt{\left(m-2\right)^2+\left(m-1\right)^2}}=\dfrac{1}{\sqrt{\left(m-2\right)^2+\left(m-1\right)^2}}\)
Để d(O;d) lớn nhất thì \(\sqrt{\left(m-2\right)^2+\left(m-1\right)^2}_{MIN}\)
\(A=\sqrt{\left(m-2\right)^2+\left(m-1\right)^2}\)
\(=\sqrt{m^2-4m+4+m^2-2m+1}\)
\(=\sqrt{2m^2-6m+5}\)
\(=\sqrt{2\left(m^2-3m+\dfrac{5}{2}\right)}\)
\(=\sqrt{2\left(m^2-3m+\dfrac{9}{4}+\dfrac{1}{4}\right)}\)
\(=\sqrt{2\left(m-\dfrac{3}{2}\right)^2+\dfrac{1}{2}}>=\dfrac{1}{\sqrt{2}}\)
Dấu = xảy ra khi m=3/2
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