Bài 4 :
a) \(A=x^2-2xy+2y^2-4y+5\)
\(\Rightarrow A=x^2-2xy+y^2+y^2-4y+4+1\)
\(\Rightarrow A=\left(x-y\right)^2+\left(y-2\right)^2+1\)
mà \(\left(x-y\right)^2\ge0;\left(y-2\right)^2\ge0,\forall x;y\in R\)
\(\Rightarrow A\ge1\Rightarrow GTNN\left(A\right)=1\left(x=y=2\right)\)
b) \(B=\dfrac{3\left(x+1\right)}{x^3+x^2+x+1}=\dfrac{3\left(x+1\right)}{x^2\left(x+1\right)+\left(x+1\right)}\)
\(=\dfrac{3\left(x+1\right)}{\left(x+1\right)\left(x^2+1\right)}=\dfrac{3}{x^2+1}\)
\(x^2\ge0\Rightarrow x^2+1\ge1\Rightarrow\dfrac{1}{x^2+1}\le1\Rightarrow\dfrac{3}{x^2+1}\le3\)
\(\Rightarrow B\le3\Rightarrow GTLN\left(B\right)=3\left(x=0\right)\)
