Question

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tìm x biết 

a) (x+3)²-x(3x+1)²+(2x+1)(4x²-2x+1)-2x²=54

b)(x+3)³-(x-3)(x²+3x+9)+6(x+1)²+3x²=-33

Answer 1

[Huỳnh Quang Sang]

a) \(\left(x+3\right)^2-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)-2x^2=54\)

=> x² + 6x + 9 - x(9x² + 6x + 1) + (2x)³ + 1³ - 2x² = 54

=> x² + 6x + 9 - 9x³ - 6x² - x + 8x³ + 1 - 2x² = 54

=> (-9x³ + 8x³) + (x² - 6x² - 2x²) + (6x - x) + (9 + 1) = 54

=> -x³ - 7x² + 5x + 10 = 54

=> -(x³ + 7x² - 5x - 10) = 54

=> phương trình vô nghiệm

b) (x + 3)³  - (x - 3)(x² + 3x + 9) + 6(x + 1)² + 3x = -33

=> x³ + 9x² + 27x + 27 - (x³ - 3³) + 6(x² + 2x + 1) + 3x = -33

=> x³ + 9x² + 27x + 27 - x³ + 27 + 6x² + 12x + 6 + 3x = -33

=> (x³ - x³) + (9x² + 6x²) + (27x + 12x + 3x) + (27 + 27 + 6) = -33

=> 15x² + 42x +  60 = -33

=> 15x² + 42x + 60 + 33 = 0

=> 15x² + 42x + 93 = 0

=> 3(5x² + 14x + 31) = 0

=> 5x² + 14x + 31 = 0

=> không tìm được x