Question

tìm x thỏa mãn:

a, (x - 1)² - (x - 1)(x + 1) = 0

b, (2x - 1)² - (2x + 1)² = 0

c, 25(x + 3)² + (1 - 5x)(1 + 5x) = 8

d, 9(x + 1)² - (3x - 2)(3x + 2) = 10

Answer 1

a) ( x - 1 )² - ( x - 1 )( x + 1 ) = 0

<=> x² - 2x + 1 - ( x² - 1 ) = 0

<=> x² - 2x + 1 - x² + 1 = 0

<=> 2 - 2x = 0

<=> 2x = 2 

<=> x = 1

b) ( 2x - 1 )² - ( 2x + 1 )² = 0

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

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

<=> -2.4x = 0

<=> -8x = 0

<=> x = 0

c) 25( x + 3 )² + ( 1 - 5x )( 1 + 5x ) = 8

<=> 5²( x + 3 )² + 1² - 25x² = 8

<=> [ 5( x + 3 ) ]² + 1 - 25x² = 8

<=> ( 5x + 15 )² + 1 - 25x² = 8

<=> 25x² + 150x + 225 + 1 - 25x² = 8

<=> 150x + 226 = 8

<=> 150x = -218

<=> x = -218/150 = -109/75

d) 9( x + 1 )² - ( 3x - 2 )( 3x + 2 ) = 10

<=> 3²( x + 1 )² - ( 9x² - 4 ) = 10

<=> [ 3( x + 1 ) ]² - 9x² + 4 = 10

<=> ( 3x + 3 )² - 9x² + 4 = 10

<=> 9x² + 18x + 9 - 9x² + 4 = 10

<=> 18x + 13 = 10

<=> 18x = -3

<=> x = -3/18 = -1/6

Answer 2

a) (x - 1)² - (x - 1)(x + 1) = 0

=> (x - 1)² - (x² - 1²) = 0

=> x² - 2.x.1 + 1² - x² + 1 = 0

=> x² - 2x + 1 - x² + 1 = 0

=> -2x + 1 + 1 = 0

=> -2x + 2 = 0

=> -2x = -2 => x = 1

b) (2x - 1)² - (2x + 1)² = 0

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

=> 0 = 0(đúng)

c) 25(x + 3)² + (1 - 5x)(1 + 5x) = 8

=> 25(x² + 2.x.3 + 3²) + (1² - (5x)²) = 8

=> 25x² + 150x + 225 + 1 - 25x² = 8

=> 150x +225 + 1 = 8

=> 150x = -218

=> x = -109/75

d) 9(x + 1)² - (3x - 2)(3x + 2) = 10

=> 9(x² + 2x + 1) - [(3x)² - 2²  ] = 10

=> 9x² + 18x + 9 - (9x² - 4) = 10

=> 9x² + 18x + 9 - 9x² + 4 = 10

=> 18x + 9 + 4 = 10

=> 18x = -3

=> x = -1/6

Answer 3

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

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

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

\(\Leftrightarrow x-1=0\)

\(\Rightarrow x=1\)

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

\(\Leftrightarrow-2.4x=0\)

\(\Rightarrow x=0\)

c) \(25\left(x+3\right)^2+\left(1-5x\right)\left(1+5x\right)=8\)

\(\Leftrightarrow25x^2+150x+225+1-25x^2-8=0\)

\(\Leftrightarrow150x=-218\)

\(\Rightarrow x=-\frac{109}{75}\)

d) \(9\left(x+1\right)^2-\left(3x-2\right)\left(3x+2\right)=10\)

\(\Leftrightarrow9x^2+18x+9-9x^2+4=10\)

\(\Leftrightarrow18x=-3\)

\(\Rightarrow x=-\frac{1}{6}\)

Answer 4

a. ( x - 1 )² - ( x - 1 ) ( x + 1 ) = 0

<=> x² - 2x + 1 - x² + 1 = 0

<=> - 2x + 2 = 0

<=> - 2x = - 2

<=> x = 1

b. ( 2x - 1 )² - ( 2x + 1 )² = 0

<=> 4x² - 4x + 1 - 4x² - 4x - 1 = 0

<=> - 8x = 0

<=> x = 0

c. 25 ( x + 3 )² + ( 1 - 5x ) ( 1 + 5x ) = 8

<=> 25x² + 150x + 225 + 1 - 25x² = 8

<=> 150x + 226 = 8

<=> 150x = - 218

<=> x = - 109/75

d. 9 ( x + 1 )² - ( 3x - 2 ) ( 3x + 2 ) = 10

<=> 9x² + 18x + 9 - 9x² + 4 = 10

<=> 18x + 13 = 10

<=> 18x = - 3

<=> x = - 1/6