Question

Tìm GTNN: A= x^2- 6x + 12

B= 4x^2 + 4x +4

Answer 1

\(A=x^2-6x+12=\left(x^2-6x+9\right)+3=\left(x-3\right)^2+3\)

Có: \(\left(x-3\right)^2\ge0\Rightarrow\left(x-3\right)^2+3\ge3\)

Dấu ''='' xảy ra khi x = 3

Vậy Min_A = 3 ⇔ x = 3

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\(B=4x^2+4x+4=\left(4x^2+4x+1\right)+3=\left(2x+1\right)^2+3\)

Vì: \(\left(2x+1\right)^2\ge0\Rightarrow\left(2x+1\right)^2+3\ge3\)

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

Vậy Min_B = 3 ⇔ x = \(-\dfrac{1}{2}\)