ä¸ã填空é¢
(1)x2+2x-15=(x-3)(_____)
(2)6xy-x2-5y2=-(x-y)(_____).
(3)________=(x+2)(x-3).
(4)å解å å¼x2+6x-7=__________.
(5)è¥å¤é¡¹å¼x2+bx+cå¯å解为(x+3)(x-4), åb=_____, c=_____.
(6)è¥x2+7x=18æç«ï¼åxå¼ä¸º_____ã
(7)è¥x2-3xy-4y2=0ï¼ä¸x+yâ 0ï¼åx=_____.
(8)(x-y)2+15(x-y)+14=(_____+1)(x-y+_____).
(9)å¤é¡¹å¼ x2+3x+2, x2-2x-8, x2+x-2çå
¬å å¼ä¸º_____ã
(10)å·²ç¥a, b为æ´æ°ï¼ä¸m2-5m-6=(m+a)(m+b), åa=_____,b=_____.
äºãéæ©é¢
(1)è¥x2+2x+y2-6y+10=0ï¼åä¸åç»ææ£ç¡®çæ¯ï¼ ï¼ã
Aãx=1, y=3 Bãx=-1,y=-3 Cãx=-1,y=3 Dãx=1,y=-3
(2)è¥x2-ax-15=(x+1)(x-15)ï¼åaçå¼æ¯ï¼ ï¼ã
Aã15 Bã-15 Cã14 Dã-14
(3)å¦æ3a-b=2,é£ä¹9a2-6ab+b2çäºï¼ ï¼ã
Aã2 Bã4 Cã6 Dã8
(4)è¥x+y=4, x2+y2=6ï¼åxyçå¼æ¯ï¼ ï¼ã
Aã10 Bã5 Cã8 Dã4
(5)å解å å¼(x2+2x)2+2(x2+2x)+1çæ£ç¡®ç»ææ¯ï¼ ï¼ã
Aã(x2+2x+1)2 Bã(x2-2x+1)2 Cã(x+1)4 Dã(x-1)4
(6)-(2x-y)(2x+y)æ¯ä¸ååªä¸ä¸ªå¤é¡¹å¼å解å å¼çç»æï¼ ï¼ã
Aã4x2-y2 Bã4x2+y2 Cã-4x2-y2 Dã-4x2+y2
(7)è¥x2+2(m-3)x+16æ¯å®å
¨å¹³æ¹å¼ï¼åmçå¼åºä¸ºï¼ ï¼ã
Aã-5 Bã7 Cã-1 Dã7æ-1
(8)å·²ç¥x3-12x+16æä¸ä¸ªå å¼ä¸ºx+4, æå®å解å å¼ååºå½æ¯ï¼ ï¼ã
Aã(x+4)(x-2)2 Bã(x+4)(x2+x+1)
Cã(x+4)(x+2)2 Dã(x+4)(x2-x+1)
ä¸ãå å¼å解
(1) x(x+y+z)+yz (2) x2m+xm+
(3) a2b2-a2-b2-4ab+1
(4) a2(x-y)2-2a(x-y)3+(x-y)4
(5) x4-6x2+5
(6) x4-7x2+1 (7) 3a8-48b8
(8) x2+4y2+9z2-4xy-6xz+12yz
åã解çé¢
1.å·²ç¥a2+9b2-2a+6b+2=0ï¼æ±a,bçå¼ã
2.æ±è¯ï¼ä¸è®ºxåä»ä¹æçæ°ï¼å¤é¡¹å¼-2x4+12x3-18x2çå¼é½ä¸ä¼æ¯æ£æ°ã
3.å·²ç¥n为æ£æ´æ°ï¼è¯è¯æ(n+5)2-(n-1)2çå¼ä¸å®è¢«12æ´é¤ã
4.å·²ç¥x+y=4, xy=3ï¼æ±(1) 3x2+3y2; (2) (x-y)2.
5.设a>0, b>0, c>0ä¸aãbãcä¸ä»»æ两æ°ä¹å大äºç¬¬ä¸ä¸ªæ°ï¼æ±è¯ï¼a2-b2-c2-2bc<0.
äºãå©ç¨å å¼å解计ç®ï¼
(1)å·²ç¥é¿æ¹å½¢çå¨é¿æ¯16cm, å®ç两边é¿aãbæ¯æ´æ°ï¼æ»¡è¶³a-b-a2+2ab-b2+2=0ï¼æ±é¿æ¹å½¢é¢ç§¯ã
(2)å¦å¾1ï¼ä¸æ¡æ°´æ¸ ï¼å
¶æ¨ªæé¢ä¸ºæ¢¯å½¢ï¼æ ¹æ®å¾ä¸çé¿åº¦ï¼æ±åºæ¨ªæé¢é¢ç§¯ç代æ°å¼ï¼å¹¶è®¡ç®åºå½a=2, b=0.8æ¶çé¢ç§¯ã
(3)å¦å¾2ï¼å¨åå¾ä¸ºRçåå½¢é¢æ¿ä¸ï¼å²å»åå¾ä¸ºrçå个å°åï¼å©ç¨å å¼å解计ç®å½R=7.8cm, r=1.1cmæ¶å©ä½é¨åçé¢ç§¯ï¼Ïå3.14ï¼ç»æä¿çä¸ä½æææ°åï¼ã
çæ¡ï¼
ä¸ã(1) x+5 (2) x-5y (3) x2-x-6
(4) (x+7)(x-1) (5) -1, -12 (6) -9æ2
(7) 4y (8) x-y, 14 (9) x+2 (10) -6æ1ï¼1æ-6
äºã(1)C (2)C (3)B (4)B (5)C (6)D (7)D (8)A
ä¸ã(1) (x+y)(x+z) (2) (xm+)2
(3) (ab-1-a-b)(ab-1+a+b)
(4) (x-y)2(a-x+y)2
(5) (x+1)(x-1)(x2-5)
(6) (x2+3x+1)(x2-3x+1)
(7) 3(a4+4b4)(a2+2b2)(a2-2b2)
(8) (x-2y-3z)2
åã1ãa=1, b=-
2ãè¯æï¼-2x4+12x3-18x2=-2x2(x2-6x+9)=-2x2(x-3)2â¤0.
3ãè¯æï¼(n+5)2-(n-1)2=(n+5+n-1)(n+5-n+1)=6(2n+4)=12(n+2).
â´ (n+5)2-(n-1)2è½è¢«12æ´é¤ã
4ã(1) 30 (2) 4
5ãæ示ï¼å°æ±è¯å·¦è¾¹åç»å解æå个æ´å¼ä¹ç§¯ï¼ç¶åå©ç¨å·²ç¥æ¡ä»¶å¯¹æ¯ä¸ªå å¼ç符å·è¿è¡è®¨è®ºã
äºã(1) ç±é¢æå¾
a+b=8, (a-b+1)(a-b-2)=0,
â´ a-b=-1æa-b=2.
âµ aä¸bæ¯æ´æ°ï¼ â´a-b=-1ä¸åé¢æã
âµ a-b=2, â´ a=5, b=3.
â´ ab=15ï¼å³é¿æ¹å½¢çé¢ç§¯ä¸º15cm2ã
(2) 3.36 (3) 176cm2
ä¸ã填空é¢
(1)x2+2x-15=(x-3)(_____)
(2)6xy-x2-5y2=-(x-y)(_____).
(3)________=(x+2)(x-3).
(4)å解å å¼x2+6x-7=__________.
(5)è¥å¤é¡¹å¼x2+bx+cå¯å解为(x+3)(x-4), åb=_____, c=_____.
(6)è¥x2+7x=18æç«ï¼åxå¼ä¸º_____ã
(7)è¥x2-3xy-4y2=0ï¼ä¸x+yâ 0ï¼åx=_____.
(8)(x-y)2+15(x-y)+14=(_____+1)(x-y+_____).
(9)å¤é¡¹å¼ x2+3x+2, x2-2x-8, x2+x-2çå
¬å å¼ä¸º_____ã
(10)å·²ç¥a, b为æ´æ°ï¼ä¸m2-5m-6=(m+a)(m+b), åa=_____,b=_____.
äºãéæ©é¢
(1)è¥x2+2x+y2-6y+10=0ï¼åä¸åç»ææ£ç¡®çæ¯ï¼ ï¼ã
Aãx=1, y=3 Bãx=-1,y=-3 Cãx=-1,y=3 Dãx=1,y=-3
(2)è¥x2-ax-15=(x+1)(x-15)ï¼åaçå¼æ¯ï¼ ï¼ã
Aã15 Bã-15 Cã14 Dã-14
(3)å¦æ3a-b=2,é£ä¹9a2-6ab+b2çäºï¼ ï¼ã
Aã2 Bã4 Cã6 Dã8
(4)è¥x+y=4, x2+y2=6ï¼åxyçå¼æ¯ï¼ ï¼ã
Aã10 Bã5 Cã8 Dã4
(5)å解å å¼(x2+2x)2+2(x2+2x)+1çæ£ç¡®ç»ææ¯ï¼ ï¼ã
Aã(x2+2x+1)2 Bã(x2-2x+1)2 Cã(x+1)4 Dã(x-1)4
(6)-(2x-y)(2x+y)æ¯ä¸ååªä¸ä¸ªå¤é¡¹å¼å解å å¼çç»æï¼ ï¼ã
Aã4x2-y2 Bã4x2+y2 Cã-4x2-y2 Dã-4x2+y2
(7)è¥x2+2(m-3)x+16æ¯å®å
¨å¹³æ¹å¼ï¼åmçå¼åºä¸ºï¼ ï¼ã
Aã-5 Bã7 Cã-1 Dã7æ-1
(8)å·²ç¥x3-12x+16æä¸ä¸ªå å¼ä¸ºx+4, æå®å解å å¼ååºå½æ¯ï¼ ï¼ã
Aã(x+4)(x-2)2 Bã(x+4)(x2+x+1)
Cã(x+4)(x+2)2 Dã(x+4)(x2-x+1)
ä¸ãå å¼å解
(1) x(x+y+z)+yz (2) x2m+xm+
(3) a2b2-a2-b2-4ab+1
(4) a2(x-y)2-2a(x-y)3+(x-y)4
(5) x4-6x2+5
(6) x4-7x2+1 (7) 3a8-48b8
(8) x2+4y2+9z2-4xy-6xz+12yz
åã解çé¢
1.å·²ç¥a2+9b2-2a+6b+2=0ï¼æ±a,bçå¼ã
2.æ±è¯ï¼ä¸è®ºxåä»ä¹æçæ°ï¼å¤é¡¹å¼-2x4+12x3-18x2çå¼é½ä¸ä¼æ¯æ£æ°ã
3.å·²ç¥n为æ£æ´æ°ï¼è¯è¯æ(n+5)2-(n-1)2çå¼ä¸å®è¢«12æ´é¤ã
4.å·²ç¥x+y=4, xy=3ï¼æ±(1) 3x2+3y2; (2) (x-y)2.
5.设a>0, b>0, c>0ä¸aãbãcä¸ä»»æ两æ°ä¹å大äºç¬¬ä¸ä¸ªæ°ï¼æ±è¯ï¼a2-b2-c2-2bc<0.
äºãå©ç¨å å¼å解计ç®ï¼
(1)å·²ç¥é¿æ¹å½¢çå¨é¿æ¯16cm, å®ç两边é¿aãbæ¯æ´æ°ï¼æ»¡è¶³a-b-a2+2ab-b2+2=0ï¼æ±é¿æ¹å½¢é¢ç§¯ã
(2)å¦å¾1ï¼ä¸æ¡æ°´æ¸ ï¼å
¶æ¨ªæé¢ä¸ºæ¢¯å½¢ï¼æ ¹æ®å¾ä¸çé¿åº¦ï¼æ±åºæ¨ªæé¢é¢ç§¯ç代æ°å¼ï¼å¹¶è®¡ç®åºå½a=2, b=0.8æ¶çé¢ç§¯ã
(3)å¦å¾2ï¼å¨åå¾ä¸ºRçåå½¢é¢æ¿ä¸ï¼å²å»åå¾ä¸ºrçå个å°åï¼å©ç¨å å¼å解计ç®å½R=7.8cm, r=1.1cmæ¶å©ä½é¨åçé¢ç§¯ï¼Ïå3.14ï¼ç»æä¿çä¸ä½æææ°åï¼ã
çæ¡ï¼
ä¸ã(1) x+5 (2) x-5y (3) x2-x-6
(4) (x+7)(x-1) (5) -1, -12 (6) -9æ2
(7) 4y (8) x-y, 14 (9) x+2 (10) -6æ1ï¼1æ-6
äºã(1)C (2)C (3)B (4)B (5)C (6)D (7)D (8)A
ä¸ã(1) (x+y)(x+z) (2) (xm+)2
(3) (ab-1-a-b)(ab-1+a+b)
(4) (x-y)2(a-x+y)2
(5) (x+1)(x-1)(x2-5)
(6) (x2+3x+1)(x2-3x+1)
(7) 3(a4+4b4)(a2+2b2)(a2-2b2)
(8) (x-2y-3z)2
åã1ãa=1, b=-
2ãè¯æï¼-2x4+12x3-18x2=-2x2(x2-6x+9)=-2x2(x-3)2â¤0.
3ãè¯æï¼(n+5)2-(n-1)2=(n+5+n-1)(n+5-n+1)=6(2n+4)=12(n+2).
â´ (n+5)2-(n-1)2è½è¢«12æ´é¤ã
4ã(1) 30 (2) 4
5ãæ示ï¼å°æ±è¯å·¦è¾¹åç»å解æå个æ´å¼ä¹ç§¯ï¼ç¶åå©ç¨å·²ç¥æ¡ä»¶å¯¹æ¯ä¸ªå å¼ç符å·è¿è¡è®¨è®ºã
äºã(1) ç±é¢æå¾
a+b=8, (a-b+1)(a-b-2)=0,
â´ a-b=-1æa-b=2.
âµ aä¸bæ¯æ´æ°ï¼ â´a-b=-1ä¸åé¢æã
âµ a-b=2, â´ a=5, b=3.
â´ ab=15ï¼å³é¿æ¹å½¢çé¢ç§¯ä¸º15cm2ã
(2) 3.36 (3) 176cm2
(7)x2ï¼9xï¼18ï¼ ã
(8)2x2ï¼5xï¼3ï¼ ã
(9)12x2ï¼50xï¼8ï¼ ã
40.å å¼å解(xï¼2)(xï¼3)ï¼(xï¼2)(xï¼4)ï¼ ã
41.å å¼å解2ax2ï¼3xï¼2axï¼3ï¼ ã
42.å å¼å解9x2ï¼66xï¼121ï¼ ã
43.å å¼å解8ï¼2x2ï¼ ã
44.å å¼å解x2ï¼xï¼14 ï¼ ã
45.å å¼å解9x2ï¼30xï¼25ï¼ ã
46.å å¼å解ï¼20x2ï¼9xï¼20ï¼ ã
47.å å¼å解12x2ï¼29xï¼15ï¼ ã
48.å å¼å解36x2ï¼39xï¼9ï¼ ã
49.å å¼å解21x2ï¼31xï¼22ï¼ ã
50.å å¼å解9x4ï¼35x2ï¼4ï¼ ã
51.å å¼å解(2xï¼1)(xï¼1)ï¼(2xï¼1)(xï¼3)ï¼ ã
52.å å¼å解2ax2ï¼3xï¼2axï¼3ï¼ ã
53.å å¼å解x(yï¼2)ï¼xï¼yï¼1ï¼ ã
54.å å¼å解(x2ï¼3x)ï¼(xï¼3)2ï¼ ã
55.å å¼å解9x2ï¼66xï¼121ï¼ ã
56.å å¼å解8ï¼2x2ï¼ ã
57.å å¼å解x4ï¼1ï¼ ã
58.å å¼å解x2ï¼4xï¼xyï¼2yï¼4ï¼ ã
59.å å¼å解4x2ï¼12xï¼5ï¼ ã
60.å å¼å解21x2ï¼31xï¼22ï¼ ã
61.å å¼å解4x2ï¼4xyï¼y2ï¼4xï¼2yï¼3ï¼ ã
62.å å¼å解9x5ï¼35x3ï¼4xï¼ ã
63.å å¼å解ä¸ååå¼ï¼
(1)3x2ï¼6xï¼ ã
(2)49x2ï¼25ï¼ ã
(3)6x2ï¼13xï¼5ï¼ ã
(4)x2ï¼2ï¼3xï¼ ã
(5)12x2ï¼23xï¼24ï¼ ã
(6)(xï¼6)(xï¼6)ï¼(xï¼6)ï¼ ã
(7)3(xï¼2)(xï¼5)ï¼(xï¼2)(xï¼3)ï¼ ã
(8)9x2ï¼42xï¼49ï¼ ã
64.9x2ï¼30xï¼kå¯å为å®å
¨å¹³æ¹å¼(3xï¼a)2ï¼åkï¼ aï¼ ã
65.è¥x2ï¼mxï¼15å¯å解为(xï¼n)(xï¼3)ï¼mãnç为æ´æ°ï¼åmï¼ nï¼ ã
66.æ±ä¸ååå¼çåæå·®æ积æåã
(1)(6512 )2ï¼(3412 )2ï¼ ã
(2)(7913 )2ï¼2Ã7913 Ã23 ï¼49 ï¼ ã
(3)1998Ã0.48ï¼798Ã0.48ï¼798Ã0.52ï¼1998Ã0.52ï¼ ã
67.å å¼å解ä¸ååå¼ï¼
(1)(xï¼2)ï¼2(xï¼2)2ï¼ ã
(2)36x2ï¼39xï¼9ï¼ ã
(3)2x2ï¼axï¼6xï¼3aï¼ ã
(4)22x2ï¼31xï¼21ï¼ ã
68.å©ç¨å¹³æ¹å·®ï¼åçå¹³æ¹æå·®çå¹³æ¹å
¬å¼ï¼å¡«å¡«ç
(1)49x2ï¼1ï¼ï¼ ï¼1ï¼ï¼ ï¼1ï¼
(2)x2ï¼26xï¼ ï¼ï¼xï¼ ï¼2
(3)x2ï¼20xï¼ ï¼ï¼xï¼ ï¼2
(4)25x2ï¼49y2ï¼ï¼5xï¼ ï¼ï¼5xï¼ ï¼
(5) ï¼66xï¼121ï¼ï¼ ï¼11ï¼2
69.å©ç¨å
¬å¼æ±ä¸ååå¼çå¼
(1)æ±5992ï¼4992ï¼ (2)æ±(7512 )2ï¼(2412 )2ï¼
(3)æ±392ï¼39Ã22ï¼112ï¼ (4)æ±172ï¼34Ã5ï¼52ï¼
(5)è¥2xï¼5yï¼13 ï¼7 ï¼xï¼4yï¼7 ï¼13 æ±2x2ï¼3xyï¼20y2ï¼
70.å å¼å解3ax2ï¼6axï¼ ã
71.å å¼å解(xï¼1)xï¼5xï¼ ã
72.å å¼å解(2xï¼1)(xï¼3)ï¼(2xï¼1)(xï¼5)ï¼
73.å å¼å解xyï¼2xï¼5yï¼10ï¼
74.å å¼å解x2y2ï¼x2ï¼y2ï¼6xyï¼4ï¼ ã
ä¸ã计ç®é¢
1.å å¼å解x3ï¼2x2ï¼2xï¼1
2.å å¼å解a2b2ï¼a2ï¼b2ï¼1
3.è¯ç¨é¤æ³å¤å«15x2ï¼xï¼6æ¯ä¸æ¯3xï¼2çåå¼ã
4.(1)å¤å«3xï¼2æ¯ä¸æ¯6x2ï¼xï¼2çå å¼ï¼ï¼ååºè®¡ç®å¼ï¼
(2)å¦ææ¯ï¼è¯·å å¼å解6x2ï¼xï¼2ã
5.aï¼19912 ï¼bï¼9912 ï¼(1)æ±a2ï¼2abï¼b2ä¹å¼ï¼ (2)a2ï¼b2ä¹å¼ï¼
6.å¤å«2xï¼1æ¯å¦4x2ï¼8xï¼3çå å¼ï¼å¦ææ¯ï¼è¯·å å¼å解4x2ï¼8xï¼3ã
7.å å¼å解(1)3ax2ï¼2xï¼3axï¼2 (2)(x2ï¼3x)ï¼(xï¼3)2ï¼2xï¼6ã
8.设6x2ï¼13xï¼k为3xï¼2çåå¼ï¼æ±kä¹å¼ã
9.å¤å«3xæ¯ä¸æ¯x2ä¹å å¼ï¼ï¼è¦è¯´æçç±ï¼
10.è¥-2x2ï¼axï¼12ï¼è½è¢«2xï¼3æ´é¤ï¼æ± (1)aï¼ï¼ (2)å°-2x2ï¼axï¼12å å¼å解ã
11.(1)å å¼å解abï¼cdï¼adï¼bc
(2)å©ç¨(1)æ±1990Ã29ï¼1991Ã71ï¼1990Ã71ï¼29Ã1991çå¼ã
12.å©ç¨å¹³æ¹å·®å
¬å¼æ±1992ï¼992ï¼ï¼
13.å©ç¨ä¹æ³å
¬å¼æ±(6712 )2ï¼(3212 )2ï¼ï¼
14.å å¼å解ä¸ååå¼ï¼
(1)(2xï¼3)(xï¼2)ï¼(xï¼1)(2xï¼3) (2)9x2ï¼66xï¼121
15.请åå¦ç¨æ¾ç»å¦è¿çåç§ä¸åå å¼å解çæ¹æ³å å¼å解16x2ï¼24xï¼9
(1)æ¹æ³1: (2)æ¹æ³2:
16.å å¼å解ä¸ååå¼ï¼
(1)4x2ï¼25 (2)x2ï¼4xyï¼4y2 (3)å©ç¨(1)(2)ä¹æ¹æ³æ±a2ï¼b2ï¼2bcï¼c2
17.å å¼å解
(1)8x2ï¼18 (2)x2ï¼(aï¼b)xï¼ab
18.å å¼å解ä¸ååå¼
(1)9x4ï¼35x2ï¼4 (2)x2ï¼y2ï¼2yzï¼z2
(3)a(b2ï¼c2)ï¼c(a2ï¼b2)
19.å å¼å解(2xï¼1)(xï¼1)ï¼(2xï¼1)(xï¼3)
20.å å¼å解39x2ï¼38xï¼8
21.å©ç¨å å¼å解æ±(6512 )2ï¼(3412 )2ä¹å¼
22.å å¼å解a(b2ï¼c2)ï¼c(a2ï¼b2)
23.aãbãcæ¯æ´æ°ï¼è¥a2ï¼b2ï¼c2ï¼4aï¼8bï¼14cï¼69ï¼0ï¼æ±aï¼2bï¼3cçå¼
24.å å¼å解7(xï¼1)2ï¼4(xï¼1)(yï¼2)ï¼20(y+2)2
25.å å¼å解xy2ï¼2xyï¼3xï¼y2ï¼2yï¼1
26.å å¼å解4x2ï¼6axï¼18a2
27.å å¼å解20a3bcï¼9a2b2cï¼20ab3c
28.å å¼å解2ax2ï¼5xï¼2axï¼5
29.å å¼å解4x3ï¼4x2ï¼25xï¼25
30.å å¼å解(1ï¼xy)2ï¼(yï¼x)2
31.å å¼å解
(1)mx2ï¼m2ï¼xï¼1 (2)a2ï¼2abï¼b2ï¼1
32.å å¼å解ä¸ååå¼
(1)5x2ï¼45 (2)81x3ï¼9x (3)x2ï¼y2ï¼5xï¼5y (4)x2ï¼y2ï¼2yzï¼z2
33.å å¼å解ï¼xy2ï¼2xyï¼3xï¼y2ï¼2yï¼1
34.å å¼å解y2(xï¼y)ï¼z2(yï¼x)
35.设xï¼1æ¯2x2ï¼axï¼3çå å¼ï¼(1)æ±aï¼ï¼ (2)æ±2x2ï¼axï¼3ï¼0ä¹äºæ ¹
36.(1)å å¼å解x2ï¼xï¼y2ï¼yï¼2xyï¼ï¼
(2)æ¿(1)è¥xï¼yï¼99æ±x2ï¼xï¼y2ï¼yï¼2xyä¹å¼ï¼
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