maths

Let √ (7 - 2√12) = √a - √b , where a > b and a , b are natural numbers.

∴ 7 - 2√12 = (√a - √b)² = a + b - 2√(ab)

Set
a + b = 7 ......(1)
{
ab = 12 ......(2)
From (1) , a = 7 - b
Substitute a = 7 - b into (2)
(7 - b)b = 12
b² - 7b + 12 = 0
(b - 3)(b - 4) = 0
b = 3 or b = 4

When b = 3 , a = 4
When b = 4 , a = 3 (rejected since a > b)∴
√ (7 - 2√12)
= √a - √b
= √4 - √3
= 2 - √3

2012-02-04 18:28:31 補充：
Method 2 :

√ (7 - 2√12)

= √ ( 4+3 - 2√4√3 )

= √ (4 - 2√4√3 + 3)

= √ (√4 - √3)²

= √4 - √3

= 2 - √3

我唔係好明...你意思係?
http://i615.photobucket.com/albums/tt234/chandaiman199111/maths54.jpg

2012-02-04 19:29:57 補充：
回上面
http://i615.photobucket.com/albums/tt234/chandaiman199111/119.jpg
hope i can help you^^

開方(7-2開方12)
=開方(4+3-4開方3)
=開方[4(1-開方3)+3] <---(開方4(1-開方3)=2(1-開方3) & 開方3本身係開方3
=2(1-開方3)+開方3
=2-2開方3+開方3
=2-開方3

2012-02-04 18:50:40 補充：
錯左 sorry!
但係 開方[4(1-開方3)+3]=2(1-開方3)+開方3=0.2679…?????