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.................

Ta có : A = x² - x + 2

=> \(A=x^2-2.x.\frac{1}{2}+\frac{1}{4}+\frac{3}{4}\)

\(\Rightarrow A=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\)

Mà : \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\)

Nên : \(A=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\forall x\)

Vậy A_min = \(\frac{3}{4}\) , dấu "=" xảy ra khi và chỉ khi x = \(\frac{1}{2}\)

A = x² - x + 2 = x² - 2.x.1 + 1² + 1 = ( x+1)² + 1

Ta có: ( x+1)² \(\ge\)0 ( với mọi x)

 => ( x+1)² + 1 \(\ge\)1  khi với mọi x)

Dấu "=" xảy ra khi ( x+1)² = 0

 => x + 1 = 0 -> x= -1

Vậy GTNN của biểu thức A = x² - x + 2 là 1 khi x = -1

A= x^x2 -x +2

2= 8/4

=> x² -2 . 1/2 x + (1/2)² + 7/4

=> (x - 1/2)² + 7/4

Không tin thì thử khai triển ra nhé!

a) \(A=2\left|x-3\right|+\left|2x-10\right|=\left|2x-3\right|+\left|10-2x\right|\ge\left|2x-3+10-2x\right|=7\)

Dấu "=" xảy ra \(\Leftrightarrow\)\(\left(2x-3\right)\left(10-2x\right)\ge0\)\(\Leftrightarrow\)\(\frac{3}{2}\le x\le5\)

b) \(B\left|\frac{1}{4}x-8\right|+\left|2-\frac{1}{4}x\right|\ge\left|\frac{1}{4}x-8+2-\frac{1}{4}x\right|=6\)

Dấu "=" xảy ra \(\Leftrightarrow\)\(\left(\frac{1}{4}x-8\right)\left(2-\frac{1}{4}x\right)\ge0\)\(\Leftrightarrow\)\(8\le x\le32\)

a: Ta có: \(A=x^2+3x+4\)

\(=x^2+2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{7}{4}\)

\(=\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\forall x\)

Dấu '=' xảy ra khi \(x=-\dfrac{3}{2}\)

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

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

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

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

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

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

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

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

B=y^2-y+1

=y^2-2*y*1/2+1/4+3/4

=(y-1/2)^2+3/4>=3/4

Dấu = xảy ra khi y=1/2

E=-x^2+x+2

=-(x^2-x-2)

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

=-(x-1/2)^2+9/4<=9/4

Dấu = xảy ra khi x=1/2