học cái này chưa nếu muốn cách CM thì cmet

[x]+[x-2]>=[x+x-2]

[x]+[x-2]>=[2x-2]

suy ra [2x-2] đạt min khi 2x-2=0 hay x=1

Ta có :

A = 2x² - 10x + 11

= 2( x² - 2.x.\(\frac{5}{2}\) + \(\frac{25}{4}\) ) - \(\frac{3}{2}\)

= 2(x - \(\frac{5}{2}\))² - \(\frac{3}{2}\)

Ta có :

(x - \(\frac{5}{2}\))^{2 \(\ge0\)}

^<=> 2(x - \(\frac{5}{2}\))^{2 \(\ge0\)}

^<=> 2(x - \(\frac{5}{2}\))² - \(\frac{3}{2}\) \(\ge-\frac{3}{2}\)

Vậy A_min = - \(\frac{3}{2}\) [ Khi (x - \(\frac{5}{2}=0=>x=\frac{5}{2}\))

Bài 2:

a: ĐKXĐ: \(x\notin\left\{0;2;-2;3\right\}\)\(A=\left(\dfrac{-\left(x+2\right)}{x-2}-\dfrac{4x^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{x+2}\right):\dfrac{x\left(x-3\right)}{x^2\left(2-x\right)}\)

\(=\dfrac{-x^2-4x-4-4x^2+x^2-4x+4}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{-x\left(x-2\right)}{x-3}\)

\(=\dfrac{-4x^2-8x}{\left(x+2\right)}\cdot\dfrac{-x}{x-3}\)

\(=\dfrac{-4x\left(x+2\right)}{x+2}\cdot\dfrac{-x}{x-3}=\dfrac{4x^2}{x-3}\)

b: Để A>0 thì x-3>0

hay x>3

bạn xài cái này gõ công thức ra đi

giúp man luôn nè : \(A=\left[\dfrac{x+2}{x^2-x}+\dfrac{x-2}{x^2+x}\right].\dfrac{x^2-1}{x^2+2}\)

a) 3 x^2 - 6x - 1

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

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

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

=3 ( x-  1 )^2 - 4 

Vì 3 ( x- 1 )^2 >=0 => 3 ( x- 1 )^2 - 4 >= 4 

VẬy GTNN là 4 khi x- 1 = 0 => x = 1 

b ) ( x- 1 )( x +2 )( x+ 3 )( x+6 )

= ( x - 1 )( x+ 6 )( x+  2 )( x+ 3 )

= ( x^2 + 5x - 6 ) . ( x^2 + 5x + 6 )

Đặt x^2 + 5x = t ta có :

  = ( t- 6 )( t+ 6 )

=  t^2 - 36

Vì t^2 >=0 => t^2 -36 >= -36 

VẬy GTNN là -36 khi x ^2 + 5x = 0 => x = 0 hoặc x = 5 

Nhớ **** 

x = 0 hoặc x = 5 

ủng hộ mk nha thanks