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I am too rusty in algebra.
I have as input in a program numbers $a$ and $b$.
I am trying to find them using the below relation:

$$a + b = X$$ $$ab=Y$$

and $X$ and $Y$ are known numbers in my program.

I can't remember how to derive $a$ or $b$.

I get something like $a^{2}-aX+Y=0$ but cant't remember how to make it so that it is something like $a=....$ ; an $b=....$ ; in my program.

Any help please?

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    $\begingroup$ From there, you could use the quadratic equation. $\endgroup$ Commented Apr 23, 2012 at 14:43

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$$a = \dfrac{X +\sqrt{X^2 - 4Y}}{2}; b = \dfrac{X -\sqrt{X^2 - 4Y}}{2}$$

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  • $\begingroup$ Thanks a lot? But how did you derive that? In my program I did this as an "optimization" trick (could do it in another way) but when I couldn't remember how to figure the solution, I was really annoyed by myself $\endgroup$
    – Jim
    Commented Apr 23, 2012 at 14:49
  • $\begingroup$ This comes from the quadratic formula. You correctly recalled $$a^2 - Xa + Y = 0$$ and then I used the quadratic formula (and the fact that $a + b = X$) $\endgroup$ Commented Apr 23, 2012 at 14:51

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