a) \(4x^3-9x=0\)

\(\Leftrightarrow x\left(4x^2-9\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\4x^2=9\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm\frac{3}{2}\end{cases}}\)

b) \(3x\left(x-2\right)-5x+10=0\)

\(\Leftrightarrow\left(3x-5\right)\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=2\end{cases}}\)

c) \(4x\left(x+3\right)-x^2+9=0\)

\(\Leftrightarrow4x\left(x+3\right)-\left(x-3\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left(3x+3\right)\left(x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-3\end{cases}}\)

d) \(\left(2x+5\right)\left(x-4\right)=\left(x-4\right)\left(5-x\right)\)

\(\Leftrightarrow\left(2x+5\right)\left(x-4\right)+\left(x-5\right)\left(x-4\right)=0\)

\(\Leftrightarrow3x\left(x-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)

e) \(16x^2-25=\left(4x-5\right)\left(2x+1\right)\)

\(\Leftrightarrow\left(4x-5\right)\left(4x+5\right)-\left(4x-5\right)\left(2x+1\right)=0\)

\(\Leftrightarrow\left(4x-5\right)\left(2x+4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{4}\\x=-2\end{cases}}\)

f) \(\left(x+\frac{1}{5}\right)^2=\frac{64}{9}\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{5}=\frac{8}{3}\\x+\frac{1}{5}=-\frac{8}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{37}{15}\\x=-\frac{43}{15}\end{cases}}\)

g) \(9\left(x+2\right)^2=\left(x+3\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}3x+6=x+3\\3x+6=-x-3\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=-3\\4x=-9\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{2}\\x=-\frac{9}{4}\end{cases}}\)

a) 4x³ - 9x = 0

<=> x( 4x² - 9 ) = 0

<=> x( 2x - 3 )( 2x + 3 ) = 0

<=> x = 0 hoặc 2x - 3 = 0 hoặc 2x + 3 = 0

<=> x = 0 hoặc x = ±3/2

b) 3x( x - 2 ) - 5x + 10 = 0

<=> 3x( x - 2 ) - 5( x - 2 ) = 0

<=> ( x - 2 )( 3x - 5 ) = 0

<=> x - 2 = 0 hoặc 3x - 5 = 0

<=> x = 2 hoặc x = 5/3

c) 4x( x + 3 ) - x² + 9 = 0

<=> 4x( x + 3 ) - ( x² - 9 ) = 0

<=> 4x( x + 3 ) - ( x - 3 )( x + 3 ) = 0

<=> ( x + 3 )[ 4x - ( x - 3 ) ] = 0

<=> ( x + 3 )( 4x - x + 3 ) = 0

<=> ( x + 3 )( 3x + 3 ) = 0

<=> x + 3 = 0 hoặc 3x + 3 = 0

<=> x = -3 hoặc x= -1

d) ( 2x + 5 )( x - 4 ) = ( x - 4 )( 5 - x )

<=> ( 2x + 5 )( x - 4 ) - ( x - 4 )( 5 - x ) = 0

<=> ( x - 4 )[ ( 2x + 5 ) - ( 5 - x ) ] = 0

<=> ( x - 4 )( 2x + 5 - 5 + x ) = 0

<=> ( x - 4 ).3x = 0

<=> x - 4 = 0 hoặc 3x = 0

<=> x = 4 hoặc x = 0

e) 16x² - 25 = ( 4x - 5 )( 2x + 1 )

<=> ( 4x - 5 )( 4x + 5 ) - ( 4x - 5 )( 2x + 1 ) = 0

<=> ( 4x - 5 )[ ( 4x + 5 ) - ( 2x + 1 ) ] = 0

<=> ( 4x - 5 )( 4x + 5 - 2x - 1 ) = 0

<=> ( 4x - 5 )( 2x + 4 ) = 0

<=> 4x - 5 = 0 hoặc 2x + 4 = 0

<=> x = 5/4 hoặc x = -2

f) ( x + 1/5 )² = 64/9

<=> ( x + 1/5 )² = ( ±8/3 )²

<=> x + 1/5 = 8/3 hoặc x + 1/5 = -8/3

<=> x = 37/15 hoặc x = -43/15

g) 9( x + 2 )² = ( x + 3 )²

<=> 3²( x + 2 )² - ( x + 3 )² = 0

<=> [ 3( x + 2 ) ]² - ( x + 3 )² = 0

<=> ( 3x + 6 )² - ( x + 3 )² = 0

<=> [ ( 3x + 6 ) - ( x + 3 ) ][ ( 3x + 6 ) + ( x + 3 ) ] = 0

<=> ( 3x + 6 - x - 3 )( 3x + 6 + x + 3 ) = 0

<=> ( 2x + 3 )( 4x + 9 ) = 0

<=> 2x + 3 = 0 hoặc 4x + 9 = 0

<=> x = -3/2 hoặc x = -9/4

-_- bài này hôm qua lm rùi

a/3x(12x - 4 ) -9x (4x -3 ) = 30 
<=> 36x^2 - 12x - 36x²+27x = 30 
<=> 15x = 30 
<=> x=2

b/  => 5x -2. x^2 + 2.x^2 -2x = 15

    => 5x -2x = 15

  => 3x = 15 => x= 5

a/3x(12x - 4 ) -9x (4x -3 ) = 30 
 36x^2 - 12x - 36x²+27x = 30 
15x = 30 

 x=2

b/  5x -2. x^2 + 2.x^2 -2x = 15

     5x -2x = 15

    3x = 15 => x= 5

b)   ( 2x - 3 ) - ( 3 - 2x )( x - 1 ) = 0

<=> ( 2x - 3 ) + ( 2x - 3 )( x - 1 ) = 0

<=> ( 2x - 3 )( 1 + x - 1 ) = 0

<=> x( 2x - 3 ) = 0

\(\Leftrightarrow\orbr{\begin{cases}x=0\\2x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{3}{2}\end{cases}}}\)

Vậy .....

a, 25x^2 - 1 - (5x -1)(x+2)=0

=> (5x)^2 - 1 + (5x-1)(x+2) = 0

=> (5x-1)(5x+1) + (5x-1)(x+2) = 0

=> (5x-1)(5x+1+x+2) = 0

=> (5x-1)(6x+3) = 0

=> \(\orbr{\begin{cases}5x-1=0\\6x+3=0\end{cases}}\)

a)     25x² - 1 - ( 5x - 1 )( x + 2 ) = 0

<=> ( 5x - 1 )( 5x + 1 ) - ( 5x - 1 )( x + 2 ) = 0

<=> ( 5x - 1 )( 5x + 1 - x - 2) = 0

<=> ( 5x - 1 )( 4x - 1 ) = 0

 \(\Leftrightarrow\orbr{\begin{cases}5x-1=0\\4x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{5}\\x=\frac{1}{4}\end{cases}}}\)

Vậy .......

a, |4+2x|=-4x

=>4+2x=-4x => 4=-4x-2x 

=>4=-6x =>x=4:-6=-2.3

vậy x =-2/3

c,ta co |x+5|+|x-3|=9

 =>x+5+x-3=9        =>x+x+5=9+3=12

                             =>2x+5=12 => 2x= 12-5 =7

                             =>x=7:2=7/2

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