\(A=x^2-6x+11\)

\(\Leftrightarrow A=x^2-2.3x+9+2\)

\(\Leftrightarrow A=\left(x-3\right)^2+2\ge2\)

\(\Leftrightarrow A_{min}=2\)

\(\Leftrightarrow x-3=0\)

\(x=3\)

a/ \(M=x^2-2.\frac{3}{2}x+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2+5\)

\(=\left(x-\frac{3}{2}\right)^2+\frac{11}{4}\ge\frac{11}{4}\)

Vậy Min M = 11/4 khi x - 3/2 = 0 => x = 3/2

b/ \(N=-\left(4x^2-\frac{2}{8}x+5\right)\)

\(=-\left[\left(2x\right)^2-2.2x.\frac{1}{16}+\left(\frac{1}{16}\right)^2-\left(\frac{1}{16}\right)^2+5\right]\)

\(=-\left(2x-\frac{1}{16}\right)^2-\frac{1279}{256}\ge-\frac{1279}{256}\)

Vậy Min N = -1279/256 khi 2x - 1/16 = 0 => 2x = 1/16 => x = 1/32

TC: B=2x² + 3x + 2

        =2(x² + \(\frac{3}{2}\)x+1)

        =2\(\left(\left(x^2+2x.\frac{3}{4}+\frac{9}{16}\right)+\frac{7}{16}\right)\)

        =2\(\left(x+\frac{3}{4}\right)^2\)+\(\frac{7}{8}\)

Vì 2\(\left(x+\frac{3}{4}\right)^2\)\(\ge\)0  với mọi x\(\)

\(\Rightarrow\)2\(\left(x+\frac{3}{4}\right)^2\) + \(\frac{7}{8}\)\(\ge\)\(\frac{7}{8}\)

Dấu"=" xảy ra \(\Leftrightarrow\) \(\left(x+\frac{3}{4}\right)^2\)=0

                     \(\Leftrightarrow\)\(x+\frac{3}{4}\)=0

                      \(\Leftrightarrow\)x=\(\frac{-3}{4}\)

Vậy....

B=2(x^2+3/2x+9/16)+7/8

2(x^2+3/4)^2+7/8

vi 2(x+3/4)^2>=

suy ra B>=7/8

dau bang say ra khu va chi khi  x+3/4=0 suy ra x=-3/4

vay gia tri nho nhat cua bieu thuc B =7/8 khi x=-3/4

d cau d tung tu tao khong doi hoi vi tao phai lam bai tap ve nha ngay mai roi nhe

 Ta có: \(x^2-2x+y^2-4y+7\)

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

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

Vì:\(\left(x-1\right)^2+\left(y-2\right)^2\ge0\forall x\)

\(\Rightarrow\left(x-1\right)^2+\left(y-2\right)^2+2\ge2\forall x\)

Dấu = xảy ra khi: \(\hept{\begin{cases}\left(x-1\right)^2=0\\\left(y-2\right)^2=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=1\\y=2\end{cases}}\)

Vậy:GTNN của bt là 2 tại x=1,y=2

cậu 1 GTNN=1 khi x=0

câu 2 GTLN =12/11 khi x=3/2

ta co : x^2-3x+5=(x+3/2)^2+11/4  => (x+3/2)^2+11/4 >hoac= 11/4 ; roi ban lay 3 chia cho ca 2 ve ta duoc : 3/(x^2-3x+5) >hoac = 12/11 ;             dau = xay ra =>max=12/11 <=>x=-3/2                                                                                                                                                                                                     chuc ban hoc tot !!!!!