Bài làm:

Ta có: \(C=3x^2-6x-1\)

\(C=3\left(x^2-2x-\frac{1}{3}\right)\)

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

\(C=3\left(x-1\right)^2-4\ge-4\left(\forall x\right)\)

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

Vậy \(Min_C=-4\Leftrightarrow x=1\)

C = 3x² - 6x - 1

= 3( x² - 2x + 1 ) - 4

= 3( x - 1 )² - 4

\(3\left(x-1\right)^2\ge0x\Rightarrow\forall3\left(x-1\right)^2-4\ge-4\)

Đẳng thức xảy ra <=> x - 1 = 0 => x = 1

=> MinC = -4 <=> x = 1

\(C=3x^2-6x-1=3\left(x-1\right)^2-4\)

Vì \(\left(x-1\right)^2\ge0\forall x\)\(\Rightarrow3\left(x-1\right)^2-4\ge-4\)

Dấu "=" xảy ra \(\Leftrightarrow3\left(x-1\right)^2=0\Leftrightarrow x-1=0\Leftrightarrow x=1\)

Vậy minC = - 4 <=> x = 1

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

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

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

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

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

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

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

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

Mình nghĩ ra câu C rồi bạn nào giúp mình nghĩ nốt câu A,B hộ mình nhé mình cảm ơn!

a:6x-5-9x^2

=-(9x^2-6x+5)

=-(9x^2-6x+1+4)

=-(3x-1)^2-4<=-4

=>A>=2/-4=-1/2

Dấu = xảy ra khi x=1/3

b: \(B=\dfrac{4x^2-6x+4-1}{2x^2-3x+2}=2-\dfrac{1}{2x^2-3x+2}\)

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

=2(x^2-2*x*3/4+9/16+7/16)

=2(x-3/4)^2+7/8>=7/8

=>-1/2x^2-3x+2<=-1:7/8=-8/7

=>B<=-8/7+2=6/7

Dâu = xảy ra khi x=3/4

\(A=\left(x+3\right)^2+2\ge2\\ A_{min}=2\Leftrightarrow x=-3\\ B=\left(x^2+3x+\dfrac{9}{4}\right)-\dfrac{29}{4}=\left(x+\dfrac{3}{2}\right)^2-\dfrac{29}{4}\ge-\dfrac{29}{4}\\ B_{min}=-\dfrac{29}{4}\Leftrightarrow x=-\dfrac{3}{2}\\ C=\left(9x^2-12x+4\right)+2017=\left(3x-2\right)^2+2017\ge2017\\ C_{min}=2017\Leftrightarrow x=\dfrac{2}{3}\)

\(4x^2+4x+6\)

\(=\left(2x\right)^2+2.2x.1+1+5\)

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

\(Min=5\Leftrightarrow2x+1=0\Rightarrow x=\frac{-1}{2}\)

\(x^2+6x+11\)

\(=x^2+2.x.3+9+2\)

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

\(Min=2\Leftrightarrow x+3=0\Rightarrow x-3\)

\(x^2-3x+1\)

\(=x^2-2.x.\frac{3}{2}+\frac{9}{4}-\frac{5}{4}\)

\(=\left(x+\frac{3}{2}\right)^2-\frac{5}{4}\le\frac{-5}{4}\)

\(MIn=\frac{-5}{4}\Leftrightarrow x+\frac{3}{2}=0\Rightarrow x=\frac{-3}{2}\)

B = 4x² + 4x - 6 = (2x)² + 2.2.x + 1 - 7 = (2x + 1)² - 7 \(\ge\)-7

             Vậy MinB = -7 khi 2x + 1 = 0 => x = -1/2 

C = x² + 6x + 11 = x² + 2.3.x + 9 + 2 = (x + 3)² + 2 \(\ge\)2

              Vậy MinC = 2 khi x + 3 = 0 => x = -3

D = x² - 3x + 1 \(=x^2-2.\frac{3}{2}.x+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2+1=\left(x-\frac{3}{2}\right)^2-\frac{5}{4}\ge-\frac{5}{4}\)

              Vậy MinD = -5/4 khi x - 3/2 = 0 => x = 3/2

bài a của  o0o I am a studious person o0o có lẽ sai

\(B=4x^2+4x-6=\left(4x^2+4x+1\right)-7=\left(2x+1\right)^2-7\)

có:\(\left(2x+1\right)^2\ge0\)

vậy GTNN của B = -7 tại x = -1/2

1/

a, \(A=4x^2-4x+5=4x^2-4x+1+4=\left(2x-1\right)^2+4\ge4\)

Dấu "=" xảy ra khi x=1/2

Vậy Amin=4 khi x=1/2

b, \(B=3x^2+6x-1=3\left(x^2+2x+1\right)-4=3\left(x+1\right)^2-4\ge-4\)

Dấu "=" xảy ra khi x=-1

Vậy Bmin = -4 khi x=-1

2/

a, \(A=10+6x-x^2=-\left(x^2-6x+9\right)+19=-\left(x-3\right)^2+19\le19\)

Dấu "=" xảy ra khi x=3

Vậy Amax = 19 khi x=3

b, \(B=7-5x-2x^2=-2\left(x^2-\frac{5}{2}x+\frac{25}{16}\right)+\frac{31}{8}=-2\left(x-\frac{5}{4}\right)^2+\frac{31}{8}\le\frac{31}{8}\)

Dấu "=" xảy ra khi x=5/4

Vậy Bmax = 31/8 khi x=5/4

\(A=\left(x^2+2\cdot\dfrac{3}{2}x+\dfrac{9}{4}\right)-\dfrac{5}{4}=\left(x+\dfrac{3}{2}\right)^2-\dfrac{5}{4}\ge-\dfrac{5}{4}\\ A_{min}=-\dfrac{5}{4}\Leftrightarrow x=-\dfrac{3}{2}\\ B=\left(x^2+2xy+y^2\right)+\left(x^2+6x+9\right)+3\\ B=\left(x+y\right)^2+\left(x+3\right)^2+3\ge3\\ B_{min}=3\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\\ C=-\left(x^2-2x+1\right)+1=-\left(x-1\right)^2+1\le1\\ C_{max}=1\Leftrightarrow x=1\)