分解下列因式：1.x^-2x-1 2.4(x-y+1)+y(y-2x) 3.a^3+1 4.4x^4-13x^+9 5.
1个回答
1题目是x^2-2x-1吧?
令x^2-2x-1=0
x1=1+√2 x2=1-√2
x^2-2x-1=(x-x1)(x-x2)=(x-1-√2)(x-1+√2)
2..4(x-y+1)+y(y-2x)
=y^2-4y+4+4x-2xy
=(y-2)^2+2x(2-y)
=(y-2)(y-2x-2)
3..a^3+1=(a+1)(a^2-a+1)
4..4x^4-13x^+9
=(x^2-1)(4x^2-9)
=(x-1)(x+1)(2x+3)(2x-3)
5..b^2+c^2+2cb+2ac+2ab
=(b+c)^2+2a(b+c)
=(b+c)(b+c+2a)
6..3x^+5xy-2y^+x+9y-4
双十字相乘法或待定系数法
（3x-y+4)(x+2y-1)
7..令x^2-2√2x-3=0
x1=√2+√5 x2=√2-√5
x^2-2√2x-3=(x-x1)(x-x2)=(x-√2+√5)(x-√2-√5)
8..令3x^+4xy-y^2=0 以x为主元
x1=(-2+√7)y/3 x2=(-2-√7)y/3
3x^+4xy-y^2=3(x-x1)(x-x2)=3[x-(-2+√7)y/3][x-(-2-√7)y/3 ]
9. (x^-2x)^-7(x^-2x)+12
=（x^2-2x-3)(x^2-2x-4)
=(x-3)(x+1)(x-1-√5)(x-1+√5)
10..x^2+x-(a^2-a)
=(x^2-a^2)+x+a
=(x+a)(x-a+1)
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