A = \(x^2-x+1\)
=\(x^2-x+\dfrac{1}{4}+\dfrac{3}{4}\)
=\(\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)
Vì \(\left(x-\dfrac{1}{2}\right)^2\ge0\forall x\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\forall x\)
\(\Rightarrow A\ge\dfrac{3}{4}\forall x\)
Vậy GTNN của A là \(\dfrac{3}{4}\) khi \(\left(x-\dfrac{1}{2}\right)^2=0\) hay x = \(\dfrac{1}{2}\)
B=\(x^2-5x-2\)
=\(x^2-5x+\dfrac{25}{4}-\dfrac{33}{4}\)
=\(\left(x-\dfrac{5}{2}\right)^2-\dfrac{33}{4}\)
Vì \(\left(x-\dfrac{5}{2}\right)^2\ge0\forall x\)
\(\Rightarrow\left(x-\dfrac{5}{2}\right)^2-\dfrac{33}{4}\ge-\dfrac{33}{4}\forall x\)
\(\Rightarrow B\ge-\dfrac{33}{4}\forall x\)
Vậy GTNN của B là \(-\dfrac{33}{4}\) khi \(\left(x-\dfrac{5}{2}\right)^2=0\) hay x=\(\dfrac{5}{2}\)
