Question

Tìm x , biết :

a. ( 2x - 1 ) ( x² - 1 + 1 ) = 2x³ - 3x² + 2

b. ( x + 2 )( x + 2 ) - ( x - 2 )(x - 2 ) = 8x

c. ( x + 1 ) ( x + 2 ) ( x + 5 ) - x³ - 8x² = 27

d. ( x + 1 ) ( x² + 2x + 4 ) - x³ - 3x² + 16 = 0

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Answer 1

a) (2x - 1)(x^2 - 1 + 1) = 2x^3 - 3x^2 + 2

(2x - 1).x^2 = 2x^3 - 3x^2 + 2

2x^3 - x^2 = 2x^3 - 3x^2 + 2

-x^2 = -3x^2 + 2

2x^2 = 2

x^2 = 1

=> x = 1; -1

b) (x + 2)(x + 2) - (x - 2)(x - 2) = 8x

(x + 2)^2 - (x - 2)^2 = 8x

x^2 + 4x + 4 - x^2 + 4x - 4 = 8x

8x = 8x

=> x thuộc N*

c) (x + 1)(x + 2)(x + 5) - x^3 - 8x^2 = 27

x^3 + 5x^2 + 2x^3 + 10x + x^2 + 5x + 2x + 10x - x^3 - x^2 = 27

17x + 10 = 27

17x = 27 - 10

17x = 17

=> x = 1

d) (x + 1)(x^2 + 2x + 4) - x^3 - 3x^2 + 16 = 0

x^3 + 2x^2 + 4x + x^2 + 2x + 4 - x^3 - 3x^2 + 16 = 0

6x + 20 = 0

6x = -20

x = -20/6

=> x = -10/3