erm
x+y=6
xy=12
x+y=6
y=6-x
sub back
xy=12
x(6-x)=12
6x-x^2=12
x^2-6x=-12
x^2-6x+12=0
quadratic formula
for
ax²+bx+c=0
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
for
x²-6x+12=0
a=1
b=-6
c=12
and remember that √-1=i
[tex]x= \frac{-(-6)+/- \sqrt{(-6)^2-4(1)(12)} }{2(1)} [/tex]
[tex]x= \frac{6+/- \sqrt{36-48} }{2} [/tex]
[tex]x= \frac{6+/- \sqrt{-12} }{2} [/tex]
[tex]x= \frac{6+/- (\sqrt{-1})(\sqrt{12}) }{2} [/tex]
[tex]x= \frac{6+/- (i)(2\sqrt{3}) }{2} [/tex]
[tex]x= \frac{6+/- 2i\sqrt{3} }{2} [/tex]
x=3+/-i√3
the numbers are 3+i√3 and 3-i√3
no real numbers tho
