Question

tìm GTNN:

3x²+6x+9

Answer 1

Ta có:\(3x^2+6x+9=3\left(x^2+2x+3\right)=3\left[\left(x^2+2x+1\right)+2\right]=3\left[\left(x+1\right)^2+2\right]\)

\(=3\left(x+1\right)^2+6\)

Vì \(3\left(x+1\right)^2\ge0\forall x\Rightarrow3\left(x+1\right)^2+6\ge6\forall x\)

Dấu "=" xảy ra khi: \(3\left(x+1\right)^2=0\Leftrightarrow x=-1\)

Vậy GTNN của \(3x^2+6x+9\) là 6 khi x = -1.

Answer 2

\(3x^{2}-6x+9\)

\(\Leftrightarrow\)\(3(x^{2}-2x+3)\)

\(\Leftrightarrow\)\(3(x^{2}-2x+1)+2\)

\(\Leftrightarrow\)\(3(x-1)^{2}+2\)

GTNN = 2. Dấu "=" xảy ra khi \(x=1\)