Math Forum :: View topic – maxvalue

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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.

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