ok so there are no real solutions for xy=15000 and x+y=5
there are immaginary solutions though so
xy=15000
x+y=5
x+y=5
y=5-x
x(5-x)=15000
-x^2+5x=15000
0=x^2-5x+15000
quadriacic formula
if ax^2+bx+c=0, then
x=\(\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}\)
x^2-5x+15000
a=1
b=-5
c=15000
x=\(\frac{-(-5)+/- \sqrt{(5)^{2}-4(1)(15000)} }{2(1)}\)
x=\(\frac{5+/- \sqrt{25-60000} }{2}\)
x=\(\frac{5+/- \sqrt{-59975} }{2}\)
x=\(\frac{5+/- 5i\sqrt{2399} }{2}\)
so the numbers are
\(\frac{5+ 5i\sqrt{2399} }{2}\) and \(\frac{5- 5i\sqrt{2399} }{2}\)
