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mathquark
Joined: 02 Oct 2004Posts: 16

Posted: Thu Jan 06, 2005 12:15 am Post subject: maxvalue



Let a, b be real numbers and a^2+b^2=120
Find the maximum integer value of a*b





Wilson
Frequent VisitorJoined: 20 Oct 2004Posts: 79

Posted: Thu Jan 06, 2005 3:21 pm Post subject: Re: maxvalue



Intuitively, for a and b to be maximum, , hence . The proof is as below:
Without loss of generality, let and .
Given
Let
Then,
Therefore f(a) attains maximum at a= , hence b=.
So the maximum integer value of ab = . 




Kenny TM~
Frequent VisitorJoined: 20 Jan 2004Posts: 141

Posted: Thu Jan 06, 2005 4:41 pm Post subject: Re: maxvalue



Wilson wrote:

Intuitively, for a and b to be maximum, , hence . The proof is as below:
Without loss of generality, let and .
Given
Let
Then,
Therefore f(a) attains maximum at a= , hence b=.
So the maximum integer value of ab = . 
(Junior Math?!) My Solution:
Consider LHS. That will attain maximum when , i.e., a = b. So ab = 60.





