利用完全平方等的公式來完成
1. (3√2-√6)^2
2. (2√10-3√5)^2
3. (3√5+2)(3√5-4)
4. (2+3√3)(2-√3)
5. (√7+2√5)(√7-4√5)
6. (3√2-√5)(3√2-5√5)
7. (2√3+4)(3√3-2)
8. (3√5-2)(4√5+3)
9. (3√5-2)(4√5-3)
10. (2√3+4)(3√3+2)
平方根 送10分
2009-02-24 12:35 am
回答 (2)
2009-02-24 1:54 am
✔ 最佳答案
1. (3√2 - √6)2
= (3√2)2 - 2(3√2)( √6) + (√6)2
= 18 - 6√12 + 6
= 24 - 6(2√3)
= 24 - 12√3
2. (2√10 - 3√5)2
= (2√10)2 - 2(2√10)(3√5) + (3√5)2
= 40 - 12√50 + 45
= 85 - 12(5√2)
= 85 - 60√2
3. (3√5 + 2)(3√5 - 4)
= 3√5(3√5 - 4) + 2(3√5 - 4)
= 45 - 12√5 + 6√5 - 8
= 37 - 6√5
4. (2 + 3√3)(2 - √3)
= 2(2 - √3) + 3√3(2 - √3)
= 4 - 2√3 + 6√3 - 9
= -5 + 4√3
5. (√7 + 2√5)(√7 - 4√5)
= √7(√7 - 4√5) + 2√5(√7 - 4√5)
= 7 - 4√35 + 2√35 - 40
= -33 - 2√35
6. (3√2 - √5)(3√2 - 5√5)
= 3√2(3√2 - 5√5) - √5(3√2 - 5√5)
= 18 - 15√10 - 3√10 + 25
= 43 - 18√10
7. (2√3 + 4)(3√3 - 2)
= 2√3(3√3 - 2) + 4(3√3 - 2)
= 18 - 4√3 + 12√3 - 8
= 10 + 8√3
8. (3√5 - 2)(4√5 + 3)
= 3√5(4√5 + 3) -2(4√5 + 3)
= 60 + 9√5 - 8√5 - 6
= 54 + √5
9. (3√5 - 2)(4√5 - 3)
= 3√5(4√5 - 3) - 2(4√5 - 3)
= 60 - 9√5 - 8√5 + 6
= 66 - 17√5
10. (2√3 + 4)(3√3 + 2)
= 2√3(3√3 + 2) + 4(3√3 + 2)
= 18 + 4√3 + 12√3 + 8
= 26 + 16√3
=
2009-02-24 1:36 am
1.
(3√2-√6)2
= (3√2)2 - 2(3√2)( √6) + (√6)2
= 18 - 6√12 + 6
= 18 - 6(2√3) + 6
= 24 - 12√3
2.
3√5(2√3 + 1)2
= 3√5[(2√3)2 + 2(2√3)(1) + (1)2]
= 3√5[12 + 4√3 + 1]
= 3√5[13 + 4√3]
= 3√5(13) + 3√5(4√3)
= 39√5 + 12√15
3.
√10(√5 - √2)2
= √10[(√5)2 - 2(√5)( √2) + (√2)2]
= √10[5 - 2√10 + 2]
= √10[7 - 2√10]
= √10(7) - √10(2√10)
= 7√10 - 20
= -20 + 7√10
4.
√6(3 + 2√2)2
= √6[(3)2 + 2(3)(2√2) + (2√2)2]
= √6[9 + 12√2 + 8]
= √6[17 + 12√2]
= √6(17) + √6(12√2)
= 17√6 + 12√12
= 17√6 + 12(2√3)
= 17√6 + 24√3
5.
(√3 - √5)2 + (√3 + √5)2
= [(√3)2 - 2(√3)(√5) + (√5)2] + [(√3)2 + 2(√3)(√5) + (√5)2]
= [3- 2√15 + 5] + [3 + 2√15 + 5]
= [8 - 2√15] + [8 + 2√15]
= 16
6.
(3√2 + 2√5)2 + (3√2 - 2√5)2
= [(3√2)2 + 2(3√2)(2√5) + (2√5)2] + [(3√2)2 - 2(3√2)(2√5) + (2√5)2]
= [18 + 12√10 + 20] + [18 - 12√10 + 20]
= [38 + 12√10] + [38 - 12√10]
= 76
7.
(1 + √2)(1 + √2 - √3)
= (1)(1 + √2 - √3) + √2(1 + √2 - √3)
= (1 + √2 + √3) + (√2 + 2 + √6)
= 1 + √2 + √3 + √2 + 2 + √6
= 3 + 2√2 + √3 + √6
8.
(√2 + √3)(√2 - √3 + 1)
= √2(√2 - √3 + 1) + √3(√2 - √3 + 1)
= 2 - √6 + √2 + √6 - 3 + √3
= -1 + √2 + √3
9.
(2√10 - 3√5)2
= (2√10)2 - 2(2√10)(3√5) + (3√5)2
= 40 - 12√50 + 45
= 85 - 12(5√2)
= 85 - 60√2
10.
(3√2 + 1)(5√2 + 2)
= 3√2(5√2 + 2) + 1(5√2 + 2)
= 30 + 6√2 + 5√2 + 2
= 32 + 11√2
2009-02-23 17:36:31 補充：
記住給20點
(3√2-√6)2
= (3√2)2 - 2(3√2)( √6) + (√6)2
= 18 - 6√12 + 6
= 18 - 6(2√3) + 6
= 24 - 12√3
2.
3√5(2√3 + 1)2
= 3√5[(2√3)2 + 2(2√3)(1) + (1)2]
= 3√5[12 + 4√3 + 1]
= 3√5[13 + 4√3]
= 3√5(13) + 3√5(4√3)
= 39√5 + 12√15
3.
√10(√5 - √2)2
= √10[(√5)2 - 2(√5)( √2) + (√2)2]
= √10[5 - 2√10 + 2]
= √10[7 - 2√10]
= √10(7) - √10(2√10)
= 7√10 - 20
= -20 + 7√10
4.
√6(3 + 2√2)2
= √6[(3)2 + 2(3)(2√2) + (2√2)2]
= √6[9 + 12√2 + 8]
= √6[17 + 12√2]
= √6(17) + √6(12√2)
= 17√6 + 12√12
= 17√6 + 12(2√3)
= 17√6 + 24√3
5.
(√3 - √5)2 + (√3 + √5)2
= [(√3)2 - 2(√3)(√5) + (√5)2] + [(√3)2 + 2(√3)(√5) + (√5)2]
= [3- 2√15 + 5] + [3 + 2√15 + 5]
= [8 - 2√15] + [8 + 2√15]
= 16
6.
(3√2 + 2√5)2 + (3√2 - 2√5)2
= [(3√2)2 + 2(3√2)(2√5) + (2√5)2] + [(3√2)2 - 2(3√2)(2√5) + (2√5)2]
= [18 + 12√10 + 20] + [18 - 12√10 + 20]
= [38 + 12√10] + [38 - 12√10]
= 76
7.
(1 + √2)(1 + √2 - √3)
= (1)(1 + √2 - √3) + √2(1 + √2 - √3)
= (1 + √2 + √3) + (√2 + 2 + √6)
= 1 + √2 + √3 + √2 + 2 + √6
= 3 + 2√2 + √3 + √6
8.
(√2 + √3)(√2 - √3 + 1)
= √2(√2 - √3 + 1) + √3(√2 - √3 + 1)
= 2 - √6 + √2 + √6 - 3 + √3
= -1 + √2 + √3
9.
(2√10 - 3√5)2
= (2√10)2 - 2(2√10)(3√5) + (3√5)2
= 40 - 12√50 + 45
= 85 - 12(5√2)
= 85 - 60√2
10.
(3√2 + 1)(5√2 + 2)
= 3√2(5√2 + 2) + 1(5√2 + 2)
= 30 + 6√2 + 5√2 + 2
= 32 + 11√2
2009-02-23 17:36:31 補充：
記住給20點
收錄日期: 2021-04-29 18:15:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090223000051KK01112