\(y=\dfrac{2x^2-6x+10}{2\left(x^2+1\right)}=\dfrac{11\left(x^2+1\right)-9x^2-6x-1}{2\left(x^2+1\right)}=\dfrac{11}{2}-\dfrac{\left(3x+1\right)^2}{2\left(x^2+1\right)}\le\dfrac{11}{2}\)
\(y_{max}=\dfrac{11}{2}\) khi \(x=-\dfrac{1}{3}\)
\(y=\dfrac{2x^2-6x+10}{2\left(x^2+1\right)}=\dfrac{x^2+1+x^2-6x+9}{2\left(x^2+1\right)}=\dfrac{1}{2}+\dfrac{\left(x-3\right)^2}{2\left(x^2+1\right)}\ge\dfrac{1}{2}\)
\(y_{min}=\dfrac{1}{2}\) khi \(x=3\)
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