高分求三个一元六次方程的六个根(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=0(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=0(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=0
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![高分求三个一元六次方程的六个根(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=0(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=0(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=0](/uploads/image/z/10201426-34-6.jpg?t=%E9%AB%98%E5%88%86%E6%B1%82%E4%B8%89%E4%B8%AA%E4%B8%80%E5%85%83%E5%85%AD%E6%AC%A1%E6%96%B9%E7%A8%8B%E7%9A%84%E5%85%AD%E4%B8%AA%E6%A0%B9%281%29x%5E6-10x%5E5%2B10x%5E4%2B80x%5E3-11x%5E2-70x%3D0%282%29x%5E6-6x%5E5-257x%5E4%2B750x%5E3%2B18544x%5E2%2B3936x-177408%3D0%283%29x%5E6-x%5E5-22x%5E4%2B35x%5E3%2B13x%5E2-22x-8%3D0)
高分求三个一元六次方程的六个根(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=0(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=0(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=0
高分求三个一元六次方程的六个根
(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=0
(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=0
(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=0
高分求三个一元六次方程的六个根(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=0(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=0(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=0
解:(1)x^6-10x^5+10x^4+80x^3-11x^2-70x=(x-7)(x-5)(x-1)x(x+1)(x+2)=0
∴x1=7,x2=5,x3=1,x4=0,x5=-1,x6=-2
(2)x^6-6x^5-257x^4+750x^3+18544x^2+3936x-177408=(x-14)(x-12)(x-3)(x+4)(x+8)(x+11)=0
∴x1=14,x2=12,x3=3,x4=-4,x5=-8,x6=-11
(3)x^6-x^5-22x^4+35x^3+13x^2-22x-8=(x^3-5x^2+3x+2)(x^3+4x^2-5x-4)=0
解方程x^3-5x^2+3x+2=0得x1=4.164247938460211,x2=-0.3913823806309005,x3=1.22713444217069
解方程x^3+4x^2-5x-4=0得x4=1.4336646297832878,x5=-4.8595233886152185,x6=-0.574141241168071
∴x1=4.164247938460211
x2=-0.3913823806309005
x3=1.22713444217069
x4=1.4336646297832878
x5=-4.8595233886152185
x6=-0.574141241168071