解
令fï¼Xï¼=x^3-3px+q
fâ²ï¼Xï¼=3x^2-3=0
å¯å¾ä¸¤ä¸ªé©»ç¹x1=-1ï¼x2=1
ç±å¾åå¯ç¥
å½fï¼-1ï¼ï¼0æè
fï¼1ï¼ï¼0æ¶ï¼fï¼Xï¼=x^3-3px+qä¸Xè½´æ1个交ç¹
fï¼-1ï¼=-1+3p+qï¼0
3p+qï¼1
æè
fï¼1ï¼=1-3p+qï¼0
-3p+qï¼-1
å½fï¼-1ï¼=0æè
fï¼1ï¼=0æ¶ï¼fï¼Xï¼=x^3-3px+qä¸Xè½´æ2个交ç¹
æ¤æ¶3p+q=1ï¼æè
-3p+q=-1
å½fï¼-1ï¼ï¼0ä¸fï¼1ï¼ï¼0æ¶ï¼fï¼Xï¼=x^3-3px+qä¸Xè½´æ3个交ç¹
æ¤æ¶ï¼3p+qï¼1ï¼ â
-3p+qï¼-1â3p-qï¼1â¡
â +â¡å¾
pï¼1/3
æ»ç»
å½pï¼1/3æ¶ï¼æ¹ç¨x^3-3px+q=0æä¸ä¸ªæ ¹
å½3p+q=1ï¼æè
-3p+q=-1æ¶ï¼æ¹ç¨x^3-3px+q=0æä¸¤ä¸ªæ ¹
å½3p+qï¼1ï¼æè
-3p+qï¼-1ï¼ä¹å¯ä»¥ç¨3p-qï¼1ï¼æ¶ï¼æ¹ç¨x^3-3px+q=0æä¸ä¸ªæ ¹
å¸æè½å¸®å©ä½ ï¼æ°å¦è¾
导å¢ä¸ºæ¨è§£çï¼ä¸ç解请追é®ï¼ç解请åæ¶é为满æåçï¼(*^__^*)
追é®è¿½çå¦ï¼å¯¹ï¼
å½pï¼0æ¶
f'(x)ï¼0
åè°ä¸åï¼å½æ°åªæä¸ä¸ªé¶ç¹
å½p=0æ¶
å½æ°åªæä¸ä¸ªé¶ç¹
å½pï¼0æ¶
é©»ç¹x=±âp
.......