Question 247795
<font face="Garamond" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 20]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ xy\ =\ 96]


Since *[tex \LARGE x\ +\ y\ =\ 20], you can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 20\ -\ y]


Giving you an expression for *[tex \LARGE x] that can be substituted anywhere you see an *[tex \LARGE x].  Here's a convenient place:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ xy\ =\ 96]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(20\ -\ y\right)y\ =\ 96]


Simplify into standard form (details left as an exercise for the student):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y^2\ -\ 20y\ + 96\ =\ 0]


Now all you have to do is solve the factorable quadratic.  You will get two positive roots.  *[tex \LARGE y] can be either number and *[tex \LARGE x] will be the other.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>