posted by Lily

Find the two numbers that multiply to the product number and add to the sum number of the following:

a)Product 563033256; Sum 51895
b)Product -43481220; Sum 28429
c)Product 2545124358; Sum -105619

I tried xy = product and x+y = sum, but it didn't work out... Can someone please help me?

  1. Count Iblis

    x+y = sum --->

    y = sum - x

    product = xy = x(sum-x) ------>

    x^2 - sum x + product = 0

    x = sum/2 ± sqrt[(sum/2)^2 - product]

    There are two solutions because interchanging x and y in the solution will yield another solution. This means that you can take:

    x = sum/2 - sqrt[(sum/2)^2 - product]

    y = sum/2 + sqrt[(sum/2)^2 - product]

  2. Lily

    sorry, but I don't get it; how can I have two different solutiuons hen I'm only supposed to have one? Still, thanks.

  3. Count Iblis

    If you have a solution and you interchange x and y then the sum and the poduct are the same, so that's another solution. This means that when we solve for x we get two solutions, the other solution bwing the value for y.

  4. Lily

    oh, okay, I get it now; thanks!

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