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http://blogs.sun.com/insidemyhead/date/20070727 Friday July 27, 2007

Maths Fun Again .. Again

Some of the folks answered this in the comments to my previous entry as the answer to x being equal to . However if that is true then what is the value of x in the following equation?

 

Getting interesting now I guess :-)



Posted by insidemyhead [Personal] ( July 27, 2007 09:17 PM ) Permalink | Comments[6]
Comments:

Here also, the value of x is Square root of 2. If you follow the steps in the previous problem, x^x^x^..to infinity = 2, then here also we get x^4=4. Simplifying, we get x^2^2=2^2. So, x^2=2. Therefore, x=Square root of 2.

Posted by Hemadri on July 30, 2007 at 02:58 PM IST #

Then does it imply that 2=4 .. :-)
Since LHS are equal in both questions, RHS should be equal? Any explanations for that part of it?

Posted by InsideMyhead on July 30, 2007 at 03:18 PM IST #

It does not imply that 2=4. Because, x alone is not in the LHS, but there is a value to the power of x. So, here the LHS is x^4=4. If x=Square root of 2. Then, (Square root of 2)^4=2. Now, the LHS and RHS are equal. Is that correct?

Posted by Hemadri on July 30, 2007 at 03:27 PM IST #

Sorry, typo in the second line. Its (Square root of 2) ^4=4.

Posted by Hemadri on July 30, 2007 at 03:30 PM IST #

No what I meant was
in my first question x^x^x ... = 2 answer as per u is x^1/2. And in the second question x^x^x....= 4 and the value of x is x^1/2.
And value of x is root 2 in both cases. What exactly is (root 2) (raised to root 2) (raised to root 2) a high number of times such that the answer could be 2 or 4. Is it the right answer?
How do you explain that it is 2 sometimes and 4 sometimes? Are these more such answers based on your solution to the question?

Posted by InsideMyhead on July 30, 2007 at 03:39 PM IST #

Your doubt is valid. Actually, I tried a solution for your first problem in all my GMAT books. Never found it. Then, obviously I googled :). In mathforum.org, I found exactly the same question for which the solution they had given is like this: Assume the whole thing x^x^x..to infinty = y. So, y=2. Then, Assume all the powers upto infinity to the base x, as y. Substitute y. It becomes, x^y=2, then. We know from the previous assumption that y=2. Substitute 2. Then it becomes x^2=2. Simplifying, we get x=root 2. Though there is ambiguity in assumption and substitutions, it gives the answer :). Because (root of 2)^2=2. Baesd on this explanation, I solved the second problem x^x^x^..to infinity=4 and the soultion I got is the same, x=root of 2. I think this applies to the powers of 2. I am not aware of other roots and odd powers.

Posted by 192.18.17.3 on July 30, 2007 at 04:16 PM IST #

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