Question

Tìm GTNN của biểu thức x² - x + 2009

Answer 1

\(A=x^2-x+2009\)

\(=x^2-x+\frac{1}{4}+2008,75\)

\(=\left(x-\frac{1}{2}\right)^2+2008,75\)

\(\left(x-\frac{1}{2}\right)^2\ge0\)

\(\Rightarrow\left(x-\frac{1}{2}\right)^2+2008,75\ge2008,75\)

Dấu ''='' xảy ra khi \(x-\frac{1}{2}=0\)

\(x=\frac{1}{2}\)

\(MinA=2008,75\Leftrightarrow x=\frac{1}{2}\)

Answer 2

Ta có :

\(x^2-x+2009\)

\(=x^2-2.x.\frac{1}{2}+\frac{1}{4}+2009-\frac{1}{4}\)

\(=\left(x-\frac{1}{2}\right)^2+\frac{8035}{4}\)

\(\left(x-\frac{1}{2}\right)^2+\frac{8035}{4}\ge\frac{8035}{4}\forall x\)

Dấu " = " xảy ra khi x = 1/2

Vậy ......