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

  • pre-calc -

    Wondering if the numbers have to be real?

    Assuming they can be complex.


    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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