Ta có : \(-4x^2+4x-5=-\left(4x^2-4x+5\right)=-\left(2x-1\right)^2-4\le-4\)

\(\Rightarrow B\ge\dfrac{15}{-4}\)

Dấu ''='' xảy ra khi x = 1/2 

Vậy GTNN B là -15/4 khi x = 1/2 

`@` `\text {Ans}`

`\downarrow`

`a)`

`3x(4x-1) - 2x(6x-3) = 30`

`=> 12x^2 - 3x - 12x^2 + 6x = 30`

`=> 3x = 30`

`=> x = 30 \div 3`

`=> x=10`

Vậy, `x=10`

`b)`

`2x(3-2x) + 2x(2x-1) = 15`

`=> 6x- 4x^2 + 4x^2 - 2x = 15`

`=> 4x = 15`

`=> x = 15/4`

Vậy, `x=15/4`

`c)`

`(5x-2)(4x-1) + (10x+3)(2x-1) = 1`

`=> 5x(4x-1) - 2(4x-1) + 10x(2x-1) + 3(2x-1)=1`

`=> 20x^2-5x - 8x + 2 + 20x^2 - 10x +6x - 3 =1`

`=> 40x^2 -17x - 1 = 1`

`d)`

`(x+2)(x+2)-(x-3)(x+1)=9`

`=> x^2 + 2x + 2x + 4 - x^2 - x + 3x + 3=9`

`=> 6x + 7 =9`

`=> 6x = 2`

`=> x=2/6 =1/3`

Vậy, `x=1/3`

`e)`

`(4x+1)(6x-3) = 7 + (3x-2)(8x+9)`

`=> 24x^2 - 12x + 6x - 3 = 7 + (3x-2)(8x+9)`

`=> 24x^2 - 12x + 6x - 3 = 7 + 24x^2 +11x - 18`

`=> 24x^2 - 6x - 3 = 24x^2 + 18x -11`

`=> 24x^2 - 6x - 3 - 24x^2 + 18x + 11 = 0`

`=> 12x +8 = 0`

`=> 12x = -8`

`=> x= -8/12 = -2/3`

Vậy, `x=-2/3`

`g)`

`(10x+2)(4x- 1)- (8x -3)(5x+2) =14`

`=> 40x^2 - 10x + 8x - 2 - 40x^2 - 16x + 15x + 6 = 14`

`=> -3x + 4 =14`

`=> -3x = 10`

`=> x= - 10/3`

Vậy, `x=-10/3`

Hello các bạn còn đó ko?

a) \(x^2-64=0\)

\(\Leftrightarrow\left(x-8\right)\left(x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

b) \(4x^2-4x+1=0\)

\(\Leftrightarrow\left(2x-1\right)^2=0\Leftrightarrow2x-1=0\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

c) \(9-6x+x^2=0\)

\(\Leftrightarrow\left(x-3\right)^2=0\)

\(\Leftrightarrow x-3=0\Leftrightarrow x=3\)

a: Ta có: \(x^2-64=0\)

\(\Leftrightarrow\left(x-8\right)\left(x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

b: Ta có: \(4x^2-4x+1=0\)

\(\Leftrightarrow\left(2x-1\right)^2=0\)

hay \(x=\dfrac{1}{2}\)

c: ta có: \(x^2-6x+9=0\)

\(\Leftrightarrow\left(x-3\right)^2=0\)

hay x=3

a,4x^2-4x+1=0

  4x^2-2x-2x+1=0

  2x (2x-1)-(2x-1)=0

  (2x-1)(2x-1)=0

  (2x-1)^2=0

=>2x-1=0 <=> x=1/2

8: =>6x^2-9x+2x-3-6x^2-12x=16

=>-19x=19

=>x=-1

Rút gọn hết ta được :

a/ 41x - 17 = -21

=> 41x = -4 => x = 4/41

b/ 34x - 17 = 0 

=> 34x = 17

=> x = 17/34 = 1/2

c/ 19x + 56 = 52 

=> 19x = -4

=> x = -4/19

d/ 20x² - 16x - 34 = 10x² + 3x - 34

=> 10x² - 19x = 0

=> x(10x - 19) = 0

=> x = 0 

hoặc 10x - 19 = 0 => 10x = 19 => x = 19/10

Vậy x = 0 ; x = 19/10

Rút gọn hết ta được :

a/ 41x - 17 = -21

=> 41x = -4 => x = 4/41

b/ 34x - 17 = 0

=> 34x = 17

=> x = 17/34 = 1/2

c/ 19x + 56 = 52

=> 19x = -4

=> x = -4/19

d/ 20x 2 - 16x - 34 = 10x 2 + 3x - 34

=> 10x 2 - 19x = 0

=> x(10x - 19) = 0

=> x = 0 hoặc 10x - 19 = 0

=> 10x = 19

=> x = 19/10

Vậy x = 0 ; x = 19/10 

a: \(-x^2+2x-4\)

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

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

\(=-\left\lbrack\left(x-1\right)^2+3\right\rbrack=-\left(x-1\right)^2-3\le-3\forall x\)

=>\(\frac{1}{-x^2+2x-4}\ge-\frac13\forall x\)

Dấu '=' xảy ra khi x-1=0

=>x=1

b: \(-4x^2+12x-13\)

\(=-\left(4x^2-12x+13\right)\)

\(=-\left(4x^2-12x+9+4\right)\)

\(=-\left\lbrack\left(2x-3\right)^2+4\right\rbrack=-\left(2x-3\right)^2-4\le-4\forall x\)

=>\(\frac{12}{-4x^2+12x-13}\ge\frac{12}{-4}=-3\forall x\)

Dấu '=' xảy ra khi 2x-3=0

=>2x=3

=>\(x=\frac32\)

c: Đặt \(A=\frac{x^2-4x-4}{x^2-4x+5}\)

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

\(=1-\frac{9}{x^2-4x+5}\)

Ta có: \(x^2-4x+5\)

\(=x^2-4x+4+1\)

\(=\left(x-2\right)^2+1\ge1\forall x\)

=>\(\frac{9}{\left(x-2\right)^2+1}\le\frac91=9\forall x\)

=>\(-\frac{9}{\left(x-2\right)^2+1}\ge-9\forall x\)

=>\(A=-\frac{9}{\left(x-2\right)^2+1}+1\ge-9+1=-8\forall x\)

Dấu '=' xảy ra khi x-2=0

=>x=2

e: Đặt \(B=\frac{x^2-2011}{4\left(x^2+1\right)}\)

\(=\frac14\cdot\frac{4x^2-8044}{4x^2+4}=\frac14\cdot\frac{x^2-2011}{x^2+1}=\frac14\left(\frac{x^2+1-2012}{x^2+1}\right)=\frac14\left(1-\frac{2012}{x^2+1}\right)\)

Ta có: \(x^2+1\ge1\forall x\)

=>\(\frac{2012}{x^2+1}\le2012\forall x\)

=>\(-\frac{2012}{x^2+1}\ge-2012\forall x\)

=>\(1-\frac{2012}{x^2+1}\ge-2012+1=-2011\forall x\)

=>\(\frac14\left(1-\frac{2012}{x^2+1}\right)\ge-\frac{2011}{4}\forall x\)

Dấu '=' xảy ra khi x=0