\(A=x^2-6x+10\)

\(\Leftrightarrow A=x^2-2\cdot x\cdot3+3^2-9+10\)

\(\Leftrightarrow A=\left(x-3\right)^2+1\ge1\)     \(\forall x\in z\)

\(\Leftrightarrow A_{min}=1khix=3\)

\(B=3x^2-12x+1\)

\(\Leftrightarrow B=\left(\sqrt{3}x\right)^2-2\cdot\sqrt{3}x\cdot2\sqrt{3}+\left(2\sqrt{3}\right)^2-12+1\)

\(\Leftrightarrow B=\left(\sqrt{3}x-2\sqrt{3}\right)^2-11\ge-11\)    \(\forall x\in z\)

\(\Leftrightarrow B_{min}=-11khix=2\)

\(A=x^4-2x^3+3x^2-4x+7\)

\(=\left(x^4-2x^3+x^2\right)+\left(2x^2-4x+2\right)+5\)

\(=\left(x^2-x\right)^2+2\left(x-1\right)^2+5\ge5\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x^2-x=0\\x-1=0\end{cases}\Rightarrow x=1}\)

Vậy \(A_{min}=5\Leftrightarrow x=1\)

D = \(-\dfrac{5}{x^2-4x+7}\)

Vì: x² - 4x + 7

= x² - 4x + 4 + 3

= (x - 2)² + 3 \(\ge\) 3 \(\forall\)x

\(\Rightarrow\) \(\dfrac{5}{\left(x-2\right)^2+3}\) \(\le\) \(\dfrac{5}{3}\) \(\forall\)x

\(\Rightarrow\) \(-\dfrac{5}{\left(x-2\right)^2+3}\)\(\ge\)-\(\dfrac{5}{3}\) \(\forall\)x

Dấu"=" xảy ra khi:

x - 2 = 0

\(\Rightarrow\) x = 2

Vậy.............

E = \(\dfrac{2x^2+4x+4}{x^2+2x+4}\)

Ta có:

\(\dfrac{2x^2+4x+4}{x^2+2x+4}\)

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

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

Vì:

x² + 2x + 4

= x² + 2x + 1 + 3

= (x + 1)² + 3 \(\ge\) 3 \(\forall\)x

\(\Rightarrow\) \(\dfrac{4}{\left(x+1\right)^2+3}\) \(\le\) \(\dfrac{4}{3}\) \(\forall\)x

\(\Rightarrow\) 2 - \(\dfrac{4}{\left(x+1\right)^2+3}\) \(\le\) \(\dfrac{2}{3}\) \(\forall\)x

Dấu "=" xảy ra khi:

x + 1 = 0

\(\Rightarrow\) x = -1

Vậy...............

F = \(\dfrac{6x+8}{x^2+1}\)

= \(\dfrac{x^2+6x+9-x^2-1}{x^2+1}\)

= \(\dfrac{\left(x+3\right)^2-\left(x^2+1\right)}{x^2+1}\)

= \(\dfrac{\left(x+3\right)^2}{x^2+1}-1\) \(\ge\) -1 \(\forall\)x

Dấu "=" xảy ra khi:

(x + 3)² = 0

\(\Rightarrow\) x + 3 = 0

\(\Rightarrow\) x = -3

Vậy.....................

a) x² - 2x + 5 = (x - 1)² + 4 >= 4

Min là 4 khi x = 1

Bài 1:

a: A=x^2-6x+10

=x^2-6x+9+1

=(x-3)^2+1>=1

Dấu = xảy ra khi x=3

b: \(B=3x^2-12x+1\)

=3(x^2-4x+1/3)

=3(x^2-4x+4-11/3)

=3(x-2)^2-11>=-11

Dấu = xảy ra khi x=2