Ta có :
\(x^2+2x+5=x^2+2x+1+4=\left(x+1\right)^2+4\)
\(\Rightarrow B=\frac{3}{\left(x+1\right)^2+4}\)
Vì \(\left(x+1\right)^2\ge0\forall x\)
\(\Rightarrow\left(x+1\right)^2+4\ge4\)
\(\Rightarrow\frac{3}{\left(x+1\right)^2+4}\le\frac{3}{4}\)
\(\Rightarrow B\le\frac{3}{4}\)
Dấu " = " xảy ra khi x = - 1
Vậy MAXB= 3 / 4 khi x = - 1