因式分解

显示全部楼层 · 2009-8-27 09:31:01

注意Sqrt[x] 表示根号x(1)无法因式分解了解方程得的是{x1 = 1/2 (-1 - Sqrt[2])}, {x2 = 1/2 (-1 + Sqrt[2])}(2) =x^3 (2 x - 3 y^2) (4 x^2 + 6 x y^2 + 9 y^4)(3) =-(2 + a) (-21 + 8 a)(4) =(-3 + x) (-2 + 3 x)(5) =(m+Sqrt[3/2])(m-Sqrt[2])(6) =(2 x - 5 y) (4 x + 7 y)(7) =(4 + x^2) (-3 + 2 x^2)(8) =(-2 + a) (1 + a) (1 - a + a^2) (4 + 2 a + a^2)(9) =(-1 + a) (1 + a) (2 + a) (4 + a)(10) =(2 + x) (6 + x) (10 + 8 x + x^2)(11) =(1 + x) (3 + x) (-3 + x^2)(12) =(-1 + x - y) (x^2 + x y + y^2)(13) =(1 - 4 x + x^2) (1 + 4 x + x^2)(14) =(a^2 - a b + b^2) (a^2 + a b + b^2) (a^4 - a^2 b^2 + b^4)

千问 · 2009-8-27 09:31:01

1)4x^2+4x-1 =(2x+1-√2)(2x+1+√2) (2)8x^6-27x^3y^6=x^2(2x-3y^2)(4x^2+6xy^2+9y^4)(3)5a-8a^2+42=(21-8a)(a+2)(4)3x^2-11x+6=(3x-2)(x-3)(5)√2m^2-(2-√3)m-√6=(√2m+√3)(m-√2)(6)8x^2-6xy-35y^2=(4x+7y)(2x-5y)(7)2x^4+5x^2-12=(2x^2-3)(x+4)=(√2x-√3)(√2x+√3)(x+4)(8)a^6-7a^3-8=(a^3-8)(a^3+1)=(a-2)(A^2+2a+4)(a+1)(a^2-a+1)(9)(a^2+3a)^2-2(a^2+3a)-8=(a^2+3a-4)(a^2+3a+2)=(a+4)(a-1)(a+1)(a+2)(10)(x^2+8x+15)(x^2+8x+7)+15=(x^2+8x+10)(x^2+8x+12)=(x^2+8x+10)(x+2)(x+6)(11)x^4+4x^3-12x-9=(x+1)(x+3)(x^2+3)(12)x^3-y^3-x^2-xy-y^2=(x-y-1)(x^2+xy+y^2)(13)x^4-14x^2+1=(x-7-4√3)(x-7+4√3)(14)a^8+a^4b^4+b^8=(a^2+ab+b^2)(a^2-ab+b^2)(a^4-a^2b^2+b^4)

千问 · 2009-8-27 09:31:01

(1)4x^2+4x-1=4x^2+4x+1-2=(2x+1)2-2=(2x+1+√2)(2x+1-√2)(2)8x^6-27x^3y^6=x3[(2x)3-(3y2)3]=x3(2x-3y2)(4x2+6xy2+9y^4)(3)5a-8a^2+42=(2+a)(21-8a)(4)3x^2-11x+6=(3x-2)(x-3)(5)√2m^2-(2-√3)m-√6=(√2m+√3)(m-√2)(6)8x^2-6xy-35y^2=(2x-5y)(4x+7y)(7)2x^4+5x^2-12=(2x2-3)(x2+4)=(√2x+√3)(√2x-√3)(x2+4)(8)a^6-7a^3-8=(a3-8)(a3+1)=(a-2)(a+1)(a2+2a+4)(a2-a+1)(9)(a^2+3a)^2-2(a^2+3a)-8=(a^2+3a-8)(a^2+3a+1)
=(a+3/2+√41/2)(a+3/2-√41/2)(a+3/2+√5/2)(a+3/2-√5/2)(10)(x^2+8x+15)(x^2+8x+7)+15=(x^2+8x)2+22(x^2+8x)+120
=(x2+8x+11)2-1=(x2+8x+12)(x2+8x+10)
=(x+6)(x+2)(x+4+√6)(x+4-√6)(11)x^4+4x^3-12x-9=(x+1)(x+3)(x2-3)==(x+1)(x+3)(x+√3)(x-√3)(12)x^3-y^3-x^2-xy-y^2=(x-y-1)(x2+xy+y2)(13)x^4-14x^2+1=(x2-4x+1)(x2+4x+1)
=(x-2+√3)(x-2-√3)(x+2+√3)(x+2-√3)(14)a^8+a^4b^4+b^8 =(a2-ab+b2)(a2+ab+b2)(a^4-a2b2+b^4)
=(a2-ab+b2)(a2+ab+b2)(a2+b2+√3ab)(a2+b2-√3ab)

千问 · 2009-8-27 09:31:01

分是很高…但题也很多…值是值…可没时间做！

千问 · 2009-8-27 09:31:01

吗呀~~赔上我小命都做不完这么多题！！天啊