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2Â¥: Originally posted by chenkaiqi at 2013-01-08 14:27:27
Èôax^4+bx^3+cx^2+dx+e=0 Áî D=-(3b^2-8ac)
¡¡¡¡E=3b^4+16a^2c^2-16abc+16a^2bd-64a^3e F=-(b^3-4abc+8a^2d)^2
¡¡¡¡A=D^2-3E,B=DE-9F,C=E^2-3DF,¦¤=B^2-4AC
¡¡¡¡1.ÈôD=E=F=0£¬Ôò·½³ÌÓÐÒ»¸öËÄÖØ¸ù¡£Ôò
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3Â¥2013-01-08 16:40:00
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Èôax^4+bx^3+cx^2+dx+e=0 Áî D=-(3b^2-8ac)
¡¡¡¡E=3b^4+16a^2c^2-16abc+16a^2bd-64a^3e F=-(b^3-4abc+8a^2d)^2
¡¡¡¡A=D^2-3E,B=DE-9F,C=E^2-3DF,¦¤=B^2-4AC
¡¡¡¡1.ÈôD=E=F=0£¬Ôò·½³ÌÓÐÒ»¸öËÄÖØ¸ù¡£Ôò
¡¡¡¡x1=x2=x3=x4=-b/4a=-2c/3b=-3c/2d=-4e/d
¡¡¡¡2.ÈôA=B=C=0£¬ÇÒDEF²»Îª0£¬Ôò·½³ÌÓÐÒ»¸öÈýÖØ¸ù¡£Ôòx1=-b/4a-F/4aD x2=x3=x4=-b/4a+3F/4aD
¡¡¡¡3.ÈôE=F=0£¬D²»ÎªÁ㣬Ôò·½³ÌÓÐÁ½¶ÔÖØ¸ù¡£
¡¡¡¡x1=x2=(-b+(-D)^(1/2))/4a x3=x4=(-b-(-D)^(1/2))/4a
¡¡¡¡4.Èô¦¤=0£¬A²»ÎªÁ㣬Ôò·½³ÌÖ»ÓÐÒ»¶ÔÖØ¸ù¡£
¡¡¡¡ÁîX1=-D+B/A,X2=-B/2A,Ôò
¡¡¡¡x1=(-b+X1^(1/2)+2X2^(1/2))/4a x2=(-b+X1^(1/2)-2X2^(1/2))/4a x3=x4=(-b+X1^(1/2))/4a
¡¡¡¡5.Èô¦¤<0,ÁîT=arccos[(2AD-3B)/2A^(3/2)]
¡¡¡¡y1=-(D+2A^(1/2)cos(T/3) y2=-(D+2A^(1/2)cos(T/3+2¦Ð/3) y3=-(D+2A^(1/2)cos(T/3-2¦Ð/3)
¡¡¡¡x1=(-b+y1^(1/2)+y2^(1/2)+y3^(1/2))/4a x2=(-b+y1^(1/2)-y2^(1/2)-y3^(1/2))/4a
¡¡¡¡x3=(-b-y1^(1/2)-y2^(1/2)+y3^(1/2))/4a x4=(-b-y1^(1/2)+y2^(1/2)-y3^(1/2))/4a
¡¡¡¡6.Èô¦¤>0
¡¡¡¡Y1=AD+(3/2)(-B+(B^2-4AC)^(1/2)) Y2=AD+(3/2)(-B-(B^2-4AC)^(1/2))
¡¡¡¡Z1=(-2D-Y1^(1/3)-Y2^(1/3)/6 Z2=3^(1/2)(Y1^(1/3)-Y2^(1/3)/6
¡¡¡¡Z=-(D+Y1^(1/3)+Y2^(1/3)/3
¡¡¡¡W1=(2Z1+2(Z1^2+Z2^2)^(1/2))^(1/2) W2=(-2Z1+2(Z1^2+Z2^2)^(1/2))^(1/2)
¡¡¡¡x1=(-b+Z^(1/2)+2W1)/4a x2=(-b+Z^(1/2)-2W1)/4a
¡¡¡¡x3=(-b-Z^(1/2)-2W2)/4a x4=(-b-Z^(1/2)+2W2)/4a
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2Â¥2013-01-08 14:27:27
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