æ
 ú
Ö
6+   æ
Ö
6+
Ö
6+¼
 
 

By Krishnan Krishnan on Thursday, August 22, 2002 - 11:00 am:
What is
  æ
 ú
Ö
(6+   æ
Ö
6+
Ö
6+¼
 
 

?
By Dan Goodman on Thursday, August 22, 2002 - 11:31 am:
Here's a hint, suppose we call the answer x, so that
x=   æ
 ú
Ö
6+   æ
Ö
6+
Ö
6+¼
 
 

. What is x2-6? What is x?
By Krishnan Krishnan on Thursday, August 22, 2002 - 11:46 am:

x2 -x-6=0 which leads to x=3. Is this okay? hearty thanks

By Chris Tynan on Thursday, August 22, 2002 - 06:56 pm:

Just to let you know, this is a past National Mathematics Competition question. The answer is as Krishnan said, 3, but what about the other root?

By Graeme Mcrae on Thursday, August 22, 2002 - 07:47 pm:

The other root is -2, which is extraneous. It was introduced when we started with


x=   ___
Ö6+x
 


and then squared both sides of the equation to get

x2=6+x

--Graeme

By Andre Rzym on Thursday, August 22, 2002 - 08:59 pm:

A more complex 'continued radical' type problem is discussed here if anyone is interested ...

Andre