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ä¸æ¬¡æ¹ç¨X^3ï¼pXï¼q=0 (pãqâR)
å¤å«å¼Î=(q/2)^2ï¼(p/3)^3
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ä¸æ¬¡æ¹ç¨aX ^3ï¼bX ^2ï¼cXï¼d=0:
令X=Yâb/(3a)代å
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X1=(Y1)^(1/3)ï¼(Y2)^(1/3)ï¼
X2= (Y1)^(1/3)Ïï¼(Y2)^(1/3)Ï^2;
X3=(Y1)^(1/3)Ï^2ï¼(Y2)^(1/3)Ïï¼
å
¶ä¸Ï=(ï¼1ï¼i3^(1/2))/2ï¼
Y(1,2)=ï¼(q/2)±((q/2)^2ï¼(p/3)^3)^(1/2)ã
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å½Î=(q/2)^2ï¼(p/3)^3>0æ¶ï¼æ¹ç¨æä¸ä¸ªå®æ ¹åä¸å¯¹å
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å½Î=(q/2)^2ï¼(p/3)^3=0æ¶ï¼æ¹ç¨æä¸ä¸ªå®æ ¹ï¼å
¶ä¸æä¸ä¸ªä¸¤éæ ¹ï¼
å½Î=(q/2)^2ï¼(p/3)^3<0æ¶ï¼æ¹ç¨æä¸ä¸ªä¸ç¸ççå®æ ¹ã
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æ¹ç¨ä¸º x^4+b·x^3+c·x^2+d·x+e=0
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P=bd-4e-c&ï¼3
Q=bcd/27+ï¼104ï¼27ï¼Â·ce-(2/27)·c-be-d
D=-4·P-27·Q
u=â(-13.5·Qï¼3/2·â(-3D))
v=â(-13.5·Qï¼3/2·â(-3D))
y=(u+v-3)ï¼3
N=ï¼1/4ï¼bï¼ï¼1/4ï¼Â·bï¼c+yï¼2yï¼4·âï½ï¼1/4ï¼Â·yï¼eï½ï¼b·âï½ï¼1/4ï¼Â·y-c+yï½
M=ï¼1/4ï¼bï¼ï¼1/4ï¼Â·bï¼c+yï¼2yï¼4·âï½ï¼1/4ï¼Â·yï¼eï½ï¼b·âï½ï¼1/4ï¼Â·y-c+yï½
å
X1ï¼ï¼1/2ï¼Â·âï¼ï¼1/4ï¼Â·bï¼cï¼yï¼ï¼ï¼1/4ï¼Â·b+ï¼1/2ï¼Â·âN
X2ï¼ï¼1/2ï¼Â·âï¼ï¼1/4ï¼Â·bï¼cï¼yï¼ï¼ï¼1/4ï¼Â·b+ï¼1/2ï¼Â·âN
X3ï¼ï¼ï¼1/2ï¼Â·âï¼ï¼1/4ï¼Â·bï¼cï¼yï¼ï¼ï¼1/4ï¼Â·b+ï¼1/2ï¼Â·âN
X4ï¼ï¼ï¼1/2ï¼Â·âï¼ï¼1/4ï¼Â·bï¼cï¼yï¼ï¼ï¼1/4ï¼Â·b+ï¼1/2ï¼Â·âN
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