Question

ÍM GTNN :

a) M = x2−6x+2018

b) N =x2−x

c) P =( x- 1) (x+3)

Answer 1

Câu a :

\(M=x^2-6x+2018\)

\(=\left(x^2-6x+9\right)+2009\)

\(=\left(x-3\right)^2+2009\ge2009\)

Vậy \(MIN_M=2009\) . Dấu \("="\) xảy ra khi \(\left(x-3\right)^2=0\Leftrightarrow x=3\)

Câu b :

\(N=x^2-x\)

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

\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

Vậy \(MIN_N=-\dfrac{1}{4}\) . Dấu \("="\) xảy ra khi \(\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x=\dfrac{1}{2}\)

Câu c :

\(P=\left(x-1\right)\left(x+3\right)\)

\(=x^2+2x-3\)

\(=\left(x^2+2x+1\right)-4\)

\(=\left(x+1\right)^2-4\ge-4\)

Vậy \(MIN_P=-4\) . Dấu \("="\) xảy ra khi \(\left(x+1\right)^2=0\Leftrightarrow x=-1\)