a) \(A=\left(x-1\right)^2\ge0\)

Dấu " = " xảy ra :

\(\Leftrightarrow x-1=0\)

\(\Leftrightarrow x=1\)

Vậy \(Min_A=0\Leftrightarrow x=1\)

b) Ta thấy : \(\left(x^2-9\right)^2\ge0\)

                   \(\left|y-2\right|\ge0\)

\(\Leftrightarrow B=\left(x^2-9\right)^2+\left|y-2\right|-1\ge-1\)

Dấu " = " xảy ra :

\(\Leftrightarrow\hept{\begin{cases}x^2-9=0\\y-2=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x\in\left\{3;-3\right\}\\y=2\end{cases}}\)

Vậy \(Min_B=-1\Leftrightarrow\left(x;y\right)\in\left\{\left(3;2\right);\left(-3;2\right)\right\}\)

c) Ta thấy : \(x^4\ge0\)

                   \(x^2\ge0\)

\(\Leftrightarrow C=x^4+3x^2+2\ge2\)

Dấu " = " xảy ra ;

\(\Leftrightarrow x=0\)

Vậy \(Min_C=2\Leftrightarrow x=0\)

d) \(D=x^2+4x-100\)

\(\Leftrightarrow D=x^2+4x+4-104\)

\(\Leftrightarrow D=\left(x+2\right)^2-104\ge-104\)

Dấu " = " xảy ra :

\(\Leftrightarrow x+2=0\)

\(\Leftrightarrow x=-2\)

Vậy \(Min_D=-104\Leftrightarrow x=-2\)

\(6,\\ a,\\ 1,A=x^2+3x+7=\left(x+\dfrac{3}{2}\right)^2+\dfrac{19}{4}\ge\dfrac{19}{4}\)

Dấu \("="\Leftrightarrow x=-\dfrac{3}{2}\)

\(2,B=\left(x-2\right)\left(x-5\right)\left(x^2-7x+10\right)=\left(x-2\right)^2\left(x-5\right)^2\ge0\)

Dấu \("="\Leftrightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)

\(b,\\ 1,A=11-10x-x^2=-\left(x+5\right)^2+36\le36\)

Dấu \("="\Leftrightarrow x=-5\)

\(x^4-2x^3+3x^2-4x+2005=\left(x^4-2x^3+x^2\right)+2\left(x^2-2x+1\right)+2003=\left(x^2-x\right)^2+2\left(x-1\right)^2+2003\)

Vì \(\left(x^2-x\right)^2\ge0\forall x,\left(x-1\right)^2\ge0\forall x\)

\(\Rightarrow x^4-2x^3+3x^2-4x+2005\ge0+0+2013=2013\)

\(ĐTXR\Leftrightarrow x=1\)

toi ko bt

A= -4 - x^2 +6x

  =-(x²-6x+9)+5

=-(x-3)²+5\(\le\)5

Dấu "=" xảy ra khi x=3

Vậy...............

B= 3x^2 -5x +7

\(=3\left(x^2-2.\frac{5}{6}x+\frac{25}{36}\right)-\frac{59}{12}\)

\(=3\left(x-\frac{5}{6}\right)^2-\frac{59}{12}\ge\frac{-59}{12}\)

Dấu "=" xảy ra khi \(x=\frac{5}{6}\)

Vậy.................

A = x²+ 3x+ 7

=x² + 2*x*3/2+9/4 + 19/4

=(x+3/2)² +19/4

ta có (x+3/2)²>0 nên (x+3/2)²+ 19/4>hoặc=19/4

=> AMin khi x+3/2=0

              =>x=-3/2