Question

[Duy Saker Hy]

1.Tìm GTNN,GTLN của E =

Answer 1

[Nguyễn Thành Trương]

\(E=\dfrac{\left(x-2\right)^2-\left(x^2+1\right)}{2\left(x^2+1\right)}\)\(=\dfrac{\left(x-2\right)^2}{2\left(x^2+1\right)}-\dfrac{1}{2}\ge\dfrac{-1}{2}\)

Vậy Emin=\(\dfrac{-1}{2}\Leftrightarrow x=2\)

\(E=\dfrac{4x^2+4-4x-1-4x^2}{2\left(x^2+1\right)}\)\(=2-\dfrac{4x^2+4x+1}{2\left(x^2+1\right)}\)=\(2-\dfrac{\left(x+\dfrac{1}{2}\right)^2}{2\left(x^2+1\right)}\le2\)

Vậy Emax=2\(\Leftrightarrow x=\dfrac{-1}{2}\)