Đáp án:

`a)x=2`

`b)x=1`

`c)x=3`

`d)x=3/2`

`e)x=1/3`

Giải thích các bước giải:

`a)5x(x-3)²-5(x-1)³+15(x-2)(x+2)=5`

`⇔5x(x²-6x+9)-5(x³-3x²+3x-1)+15(x²-4)=5`

`⇔5x³-30x²+45x-5x³+15x²-15x+5+15x²-60=5`

`⇔(5x³-5x³)+(-30x²+15x²+15x²)+(45x-15x)+(5-60)=5`

`⇔30x-55=5`

`⇔30x=5+55`

`⇔30x=60`

`⇔x=60:30`

`⇔x=2`

Vậy `x=2`

`b)(2x-3)³-4x(2x-9)=27`

`⇔8x³-36x²+54x-27-8x²+36x=27`

`⇔8x³-36x²+54x-27-8x²+36x-27=0`

`⇔8x³-(36x²+8x²)+(54x+36x)-(27+27)=0`

`⇔8x³-44x²+90x-54=0`

`⇔2(4x³-22x²+45x-27)=0`

`⇔4x³-22x²+45x-27=0`

`⇔4x³-18x²-4x²+27x+18x-27=0`

`⇔(4x³-18x²+27x)-(4x²-18x+27)=0`

`⇔x(4x²-18x+27)-(4x²-18x+27)=0`

`⇔(x-1)(4x²-18x+27)=0`

`⇔(x-1)(4x²-18x+81/4+27/4)=0`

`⇔(x-1)[(4x²-18x+81/4)+27/4]=0`

`⇔(x-1){[(2x)²-2.2x. 9/2+(9/2)^2]+27/4}=0`

`⇔(x-1)[(2x-9/2)^2+27/4]=0`

Ta có:`(2x-9/2)^2≥0∀x`

`⇒(2x-9/2)^2+27/4≥27/4>0∀x`

`⇒` vô nghiệm

`⇔x-1=0`

`⇔x=1`

Vậy `x=1`

`c)(x-2)³+6(x+1)²-(x-3)(x²+3x+9)=97`

`⇔x³-6x²+12x-8+6(x²+2x+1)-(x³-27)=97`

`⇔x³-6x²+12x-8+6x²+12x+6-x³+27=97`

`⇔(x³-x³)+(-6x²+6x²)+(12x+12x)+(-8+6+27)=97`

`⇔24x+25=97`

`⇔24x=97-25`

`⇔24x=72`

`⇔x=72:24`

`⇔x=3`

Vậy `x=3`

`d)(x-1)(x²+x+1)-x(x+2)(x-2)=5`

`⇔x³-1³-x(x²-2²)=5`

`⇔x³-1-x(x²-4)=5`

`⇔x³-1-x³+4x=5`

`⇔4x-1=5`

`⇔4x=5+1`

`⇔4x=6`

`⇔x=6/4`

`⇔x=3/2`

Vậy `x=3/2`

`e)(x+1)³-x²(x+3)=2`

`⇔x³+3x²+3x+1-x³-3x²=2`

`⇔(x³-x³)+(3x²-3x²)+3x+1=2`

`⇔3x+1=2`

`⇔3x=2-1`

`⇔3x=1`

`⇔x=1/3`

Vậy `x=1/3`

Đáp án:

 `a, 5x(x - 3)^2 - 5(x - 1)^3 + 15(x - 2)(x + 2) = 5`

`⇔ 5x(x^2 - 6x + 9) - 5(x^3 - 3x^2 + 3x - 1) + 15(x^2 - 2^2) = 5`

`⇔ 5x^3 - 30x^2 + 45x - 5x^3 + 15x^2 - 15x + 5 + 15x^2 - 60 = 5`

`⇔ (5x^3 - 5x^3) + (-30x^2 + 15x^2 + 15x^2) + (45x - 15x) + (5 - 60) = 5`

`⇔ 30x - 55 = 5`

`⇔ 30x = 5 + 55 = 60`

`⇒ x = 60 : 30`

`⇒ x = 2`

Vậy `x= 2`

`b, (2x - 3)^3 - 4x(2x - 9) = 27`

`⇔ (2x)^3 - 3.(2x)^2 . 3 + 3.2x.3^2 - 3^3 - 8x^2 + 36x = 27`

`⇔ 8x^3 - 36x^2 + 54x - 27 - 8x^2 + 36x = 27`

`⇔ 8x^3 + (-36x^2 - 8x^2) + (54x + 36x) - 27 - 27 = 0`

`⇔ 8x^3 - 44x^2 + 90x - 54 = 0`

`⇔ 2(4x^3 - 22x^2 + 45x - 27) = 0`

`⇔ 4x^3 - 22x^2 + 45x - 27 = 0`

`⇔ 4x^3 - 4x^2 - 18x^2 + 18x + 27x - 27 = 0`

`⇔ 4x^2 (x - 1) - 18x(x - 1) + 27(x - 1) = 0`

`⇔ (x - 1)(4x^2 - 18x + 27) = 0`

`⇔ (x - 1)(4x^2 - 18x + 81/4 + 27/4) = 0`

`⇔ (x - 1)[(2x)^2 - 2.2x . 9/2 + (9/2)^2 + 27/4) = 0`

`⇔ (x - 1)[(2x - 9/2)^2 + 27/4) = 0`

`⇔ x - 1 = 0` (vì `[(2x - 9/2)^2 + 27/4 ≥ 27/4 > 0`)

`⇒ x = 1`

Vậy `x = 1`

`c, (x - 2)^3 + 6(x + 1)^2 - (x - 3)(x^2 + 3x + 9) = 97`

`⇔ x^3 - 3.x^2 . 2 + 3.x.2^2 - 8 + 6(x^2 + 2x + 1) - (x^3 - 3^3) = 97`

`⇔ x^3 - 6x^2 + 12x - 8 + 6x^2 + 12x + 6 - x^3 + 27 = 97`

`⇔ (x^3 - x^3) + (-6x^2 + 6x^2) + (12x + 12x) + (- 8 + 6 + 27) = 97`

`⇔ 24x + 25 = 97`

`⇔ 24x = 97 - 25 = 72`

`⇒ x = 72 : 24`

`⇒ x = 3`

Vậy `x = 3`

`d, (x - 1)(x^2 + x + 1) - x(x + 2)(x - 2) = 5`

`⇔ x^3 - 1^3 - x(x^2 - 2^2) = 5`

`⇔ x^3 - 1 - x(x^2 - 4) = 5`

`⇔ x^3 - 1 - x^3 + 4x = 5`

`⇔ (x^3 - x^3) + 4x - 1 = 5`

`⇔ 4x - 1 = 5`

`⇔ 4x = 5 + 1 = 6`

`⇔ x = 6/4 = 3/2`

Vậy `x = 3/2`

`e, (x + 1)^3 - x^2 (x + 3) = 2`

`⇔ x^3 + 3x^2 + 3x + 1 - x^3 - 3x^2 = 2`

`⇔ (x^3 - x^3) + (3x^2 - 3x^2) + 3x + 1 = 2`

`⇔ 3x + 1 = 2`

`⇔ 3x = 2 - 1 = 1`

`⇔ x = 1/3`

Vậy `x = 1/3`