Question

Tìm GTLN/GTNN:

B=\(\dfrac{2}{2x^2+4x+9}\)

Answer 1

\(B=\dfrac{2}{2\left(x^2+2x+1\right)+7}=\dfrac{2}{2\left(x+1\right)^2+7}\le\dfrac{2}{7}\) (do \(2\left(x+1\right)^2\ge0;\forall x\))

\(B_{max}=\dfrac{2}{7}\) khi \(x+1=0\Leftrightarrow x=-1\)

\(B_{min}\) ko tồn tại

Answer 2

\(2x^2+4x+9=2\left(x^2+2x+\dfrac{9}{2}\right)\)

\(=2\left(x^2+2x+1+\dfrac{7}{2}\right)\)

\(=2\left(x+1\right)^2+7\)

\(\Leftrightarrow B< =\dfrac{2}{7}\)

Dấu '=' xảy ra khi x=-1