Posted by **seria** on Monday, January 28, 2013 at 12:01am.

The sum of two numbers is radical 3. Find the largest possible value for their product

- pre-calc -
**bobpursley**, Monday, January 28, 2013 at 1:08am
Wondering if the numbers have to be real?

Assuming they can be complex.

M=10000000i+sqrt3

N=-10000000i

the sum of M+N=sqrt3

MN=10^7m and if course no limit on that, so no limit on the product.

Now if M,N are restricted to the real domain.

let V=MN=(sqrt3-N)N

dV/dN=sqrt3-2N setting equal to zero to maximize, then N= .5 sqrt3

and M= N, same value, so MN=3/4

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