2x^4-3x^3-6x^2+3x+2=0 3x^4-4x^3-10x^2+42x^4-3x^3-6x^2+3x+2=03x^4-4x^3-10x^2+4x+3=0
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2x^4-3x^3-6x^2+3x+2=03x^4-4x^3-10x^2+42x^4-3x^3-6x^2+3x+2=03x^4-4x^3-10x^2+4x+3=02x^4-3x^3-6x^2+3x+2
2x^4-3x^3-6x^2+3x+2=0 3x^4-4x^3-10x^2+42x^4-3x^3-6x^2+3x+2=03x^4-4x^3-10x^2+4x+3=0
2x^4-3x^3-6x^2+3x+2=0 3x^4-4x^3-10x^2+4
2x^4-3x^3-6x^2+3x+2=0
3x^4-4x^3-10x^2+4x+3=0
2x^4-3x^3-6x^2+3x+2=0 3x^4-4x^3-10x^2+42x^4-3x^3-6x^2+3x+2=03x^4-4x^3-10x^2+4x+3=0
这两个方程都有个特点:高低项系数是对称相等或互为相反数的.
可用以下代换方法解得.
令t=x-1/x,则有t^2+2=x^2+1/x^2
2x^4-3x^3-6x^2+3x+2=0
两边同时除以x^2,得:2(x^2+1/x^2)-3(x-1/x)-6=0
代入t,得:2(t^2+2)-3t-6=0
2t^2-3t-2=0
(2t+1)(t-2)=0
t=-0.5,2
再将t=x-1/x化为2次方程:x^2-tx-1=0.即解得x.
t=-0.5时,x=(-0.5+√4.25)/2,(-0.5-√4.25)/2
t=2时,x=1+√2,1-√2
3x^4-4x^3-10x^2+4x+3=0
也一样,化为3(x^2+1/x^2)-4(x-1/x)-10=0
3(t^2+2)-4t-10=0
3t^2-4t-4=0
(3t+2)(t-2)=0
t=-2/3,2
t=-2/3时,x=-1/3+√10/3,-1/3-√10/3
t=2时,x=1+√2,1-√2
*-----------------------------------------------*| 6 4 X | 8 X X | X X 5 || X X X | X X X | X 7 8 || X X X | X X X | X X X ||---------------+---------------+--------------- || X X X | X X X | 5 1 X || X X X | X 6 X | X X X || 8 X X | 3 5 X | 2 X X ||
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