one way is to expand theh 18
and multily them
117=17, nope
216=32, nope
315=45, nope
414=56, nope
513=65, nope
612=72, nope
711=77, nope
810=80, nope
9*9=81, nope
so we aren't going to get it that way
xy=108
x+y=18
solve for 1
minus x both sides in 2nd equation
y=18-x
sub 18-x for y in other equaiton
x(18-x)=108
18x-x²=108
times -1 both sides
x²-18x=-108
add 108 both sides
x²-18x+108=0
we know we can't factor so we has to use quadratic formula
for
ax²+bx+c=0
x=\(\frac{-b+/- \sqrt{b^2-4ac} }{2a}\)
given
1x²-18x+108
a=1
b=-18
c=108
rememeber that √-1=i
x=\(\frac{-(-18)+/- \sqrt{(-18)^2-4(1)(108)} }{2(1)}\)
x=\(\frac{18+/- \sqrt{324-432} }{2}\)
x=\(\frac{18+/- \sqrt{-108} }{2}\)
x=\(\frac{18+/- (\sqrt{36})(\sqrt{3})(\sqrt{-1}) }{2}\)
x=\(\frac{18+/- (6)(\sqrt{3})(i) }{2}\)
\(x=9+/-3i \sqrt{3}\)
the numbers are 9+3i√3 and 9-3i√3
