几道因式分解、解方程,(1)2x^3+3x^2-8x+3=0 (2)m^2-√3m-6=0(3)27a^3-27a^2b+9ab^2-b^3-1

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几道因式分解、解方程,(1)2x^3+3x^2-8x+3=0 (2)m^2-√3m-6=0(3)27a^3-27a^2b+9ab^2-b^3-1

几道因式分解、解方程,(1)2x^3+3x^2-8x+3=0 (2)m^2-√3m-6=0(3)27a^3-27a^2b+9ab^2-b^3-1
几道因式分解、解方程,(1)2x^3+3x^2-8x+3=0 (2)m^2-√3m-6=0
(3)27a^3-27a^2b+9ab^2-b^3-1

几道因式分解、解方程,(1)2x^3+3x^2-8x+3=0 (2)m^2-√3m-6=0(3)27a^3-27a^2b+9ab^2-b^3-1
1.
2x^3+3x^2-8x+3=0
(2x^3-2x)+(3x^2-6x+3)=0
2x(x+1)(x-1)+3(x-1)^2=0
(x-1)(2x^2+5x-3)=0
(x-1)[(2x^2+6x)-(x+3)]=0
(x-1)[2x(x+3)-(x+3)]=0
(x-1)(x+3)(2x-1)=0
所以方程的解是:
x=1、x=-3、x=1/2
2.
m^2-√3m-6=0
[m-(√3)/2]^2-3/4-6=0
[m-(√3)/2]^2=27/4
所以:
m-(√3)/2=±[(3/2)*√3]
所以:
m=(√3)/2±[(3/2)*√3]
所以方程的解是:
m=2√3、m=-√3
3.
27a^3-27a^2b+9ab^2-b^3-1
=(3a-b-1)(9a^2-6ab+3a+b^2-b+1)

1)

2x^3+3x^2-6x+3-2x=0

2x^3+3(x-1)^2-2x=0

2x(x^2-1) +3(x-1)^2=0

2x(x+1)(x-1) +3(x-1)^2=0

(x-1)[2x(x+1)+3(x-1)]=0

(x-1)(2x^2+5x-3)=0

x=1; x=-3/2;x=-2

2)