precalc
posted by seria on .
The sum of two numbers is radical 3. Find the largest possible value for their product

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=(sqrt3N)N
dV/dN=sqrt32N setting equal to zero to maximize, then N= .5 sqrt3
and M= N, same value, so MN=3/4