鍒濅腑鏁板绔炶禌涓撻鍩硅
绗叓璁?/p>
闈炶礋鏁?/p>
鎵�璋撻潪璐熸暟锛屾槸鎸囬浂鍜屾瀹炴暟锛庨潪璐熸暟鐨勬�ц川鍦ㄨВ棰樹腑棰囨湁
鐢ㄥ锛庡父瑙佺殑闈炶礋鏁版湁涓夌锛氬疄鏁扮殑鍋舵骞傘�佸疄鏁扮殑缁濆鍊煎拰绠?/p>
鏈牴锛?/p>
1
锛庡疄鏁扮殑鍋舵骞傛槸闈炶礋鏁?/p>
鑻?/p>
a
鏄换鎰忓疄鏁帮紝鍒?/p>
a
2n
鈮?/p>
0(n
涓烘鏁存暟
)
锛岀壒鍒湴锛屽綋
n=1
鏃讹紝鏈?/p>
a
2
鈮?/p>
0
锛?/p>
2
锛庡疄鏁扮殑缁濆鍊兼槸闈炶礋鏁?/p>
鑻?/p>
a
鏄疄鏁帮紝鍒?/p>
鎬ц川
缁濆鍊兼渶灏忕殑瀹炴暟鏄浂锛?/p>
`
3
锛庝竴涓瀹炴暟鐨勭畻鏈牴鏄潪璐熸暟
4
锛庨潪璐熸暟鐨勫叾浠栨�ц川
(1)
鏁拌酱涓婏紝鍘熺偣鍜屽師鐐瑰彸杈圭殑鐐硅〃绀虹殑鏁伴兘鏄潪璐熸暟锛?/p>
(2)
鏈夐檺涓潪璐熸暟鐨勫拰浠嶄负闈炶礋鏁帮紝鍗宠嫢
a
1
锛?/p>
a
2
锛屸�烇紝
a
n
涓洪潪璐熸暟锛?/p>
鍒?/p>
a
1
锛?/p>
a
2
锛嬧�烇紜
a
n
鈮?/p>
0
锛?/p>
(3)
鏈夐檺涓潪璐熸暟鐨勫拰涓洪浂锛?/p>
閭ｄ箞姣忎竴涓姞鏁颁篃蹇呬负闆讹紝
鍗宠嫢
a
1
锛?/p>
a
2
锛屸�烇紝
a
n
涓洪潪璐熸暟锛屼笖
a
1
锛?/p>
a
2
锛嬧�烇紜
a
n
=0
锛屽垯蹇呮湁
a
1
锛?/p>
a
2
锛濃�?/p>
锛?/p>
a
n
锛?/p>
0
锛?/p>
鍦ㄥ埄鐢ㄩ潪璐熸暟瑙ｅ喅闂鐨勮繃绋嬩腑锛岃繖鏉℃�ц川浣跨敤鐨勬渶澶氾紟
(4)
闈炶礋鏁扮殑绉拰鍟?/p>
(
闄ゆ暟涓嶄负闆?/p>
)
浠嶄负闈炶礋鏁帮紟
(5)
鏈�灏忛潪璐熸暟涓洪浂锛屾病鏈夋渶澶х殑闈炶礋鏁帮紟
(6)
涓�鍏冧簩娆℃柟绋?/p>
ax
2
锛?/p>
bx
锛?/p>
c=0(a
鈮?/p>
0)
鏈夊疄鏁版牴鐨勫厖瑕佹潯浠?/p>
鏄垽鍒紡鈻?/p>
=b
2
-
4ac
涓洪潪璐熸暟锛?/p>
搴旂敤闈炶礋鏁拌В鍐抽棶棰樼殑鍏抽敭鍦ㄤ簬鑳藉惁璇嗗埆骞舵彮绀哄嚭棰樼洰涓殑
闈炶礋鏁帮紝姝ｇ‘杩愮敤闈炶礋鏁扮殑鏈夊叧姒傚康鍙婂叾鎬ц川锛屽阀濡欏湴杩涜鐩稿簲
鍏崇郴鐨勮浆鍖栵紝浠庤�屼娇闂寰楀埌瑙ｅ喅锛?/p>
瑙ｅ緱
a=3
锛?/p>
b=
-
2
锛庝唬鍏ヤ唬鏁板紡寰?/p>
瑙?/p>
鍥犱负
(20x
-
3)
2
涓洪潪璐熸暟锛屾墍浠?/p>
-
(20x
-
3)
2
鈮?/p>
0
锛?/p>
鈶?/p>
-
(20x
-
3)
2
鈮?/p>
0
锛?/p>
鈶?/p>
鐢扁憼锛屸憽鍙緱锛?/p>
-
(20x
-
3)
2
=0
锛庢墍浠?/p>
鍘熷紡
=
锝滐綔
20
卤
0
锝滐紜
20
锝?/p>
=40
锛?/p>
璇存槑
鏈瑙ｆ硶涓簲鐢ㄤ簡鈥滆嫢
a
鈮?/p>
0
涓?/p>
a
鈮?/p>
0
锛屽垯
a=0
鈥濓紝杩欐槸
涓緢鏈夌敤鐨勬�ц川锛?/p>
渚?/p>
3
宸茬煡
x
锛?/p>
y
涓哄疄鏁帮紝
瑙?/p>
鍥犱负
x
锛?/p>
y
涓哄疄鏁帮紝瑕佷娇
y
鐨勮〃杈惧紡鏈夋剰涔夛紝蹇呮湁
瑙?/p>
鍥犱负
a
2
+b
2
-
4a
-
2b+5=0
锛屾墍浠?/p>
a
2
-
4a+4+b
2
-
2b+1=0
锛?/p>
鍗?/p>
(a
-
2)
2
+(b
-
1)
2
=0
锛?/p>
(a
-
2)
2
=0
锛屼笖
(b
-
1)
2
=0
锛?/p>
鎵�浠?/p>
a=2
锛?/p>
b=1
锛庢墍浠?/p>
渚?/p>
5
宸茬煡
x
锛?/p>
y
涓哄疄鏁帮紝姹?/p>
u=5x
2
-
6xy+2y
2
+2x
-
2y+3
鐨勬渶灏忓�煎拰鍙栧緱鏈�灏忓�兼椂鐨?/p>
x
锛?/p>
y
鐨勫�硷紟
瑙?/p>
u=5x
2
-
6xy+2y
2
+2x
-
2y+3
=x
2
+y
2
+1
-
2xy+2x
-
2y+4x
2
-
4xy+yg2+2
=(x
-
y+1)
2
+(2x
-
y)
2
+2
锛?/p>
鍥犱负
x
锛?/p>
y
涓哄疄鏁帮紝鎵�浠?/p>
(x
-
y+1)
2
鈮?/p>
0
锛?/p>
(2x
-
y)
2
鈮?/p>
0
锛屾墍浠?/p>
u
鈮?/p>
2
锛庢墍浠ュ綋
鏃讹紝
u
鏈夋渶灏忓�?/p>
2
锛屾鏃?/p>
x=1
锛?/p>
y=2
锛?/p>
渚?/p>
6
纭畾鏂圭▼
(a
2
+1)x
2
-
2ax+(a
2
+4)=0
鐨勫疄鏁版牴鐨勪釜鏁帮紟
瑙?/p>
灏嗗師鏂圭▼鍖栦负
a
2
x
2
-
2ax+1+x
2
+a
2
+3=0
锛?/p>
鍗?/p>
(ax
-
1)
2
+x
2
+a
2
+3=0
锛?/p>
瀵逛簬浠绘剰瀹炴暟
x
锛屽潎鏈?/p>