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Dmitry [639]
3 years ago
9

What two numbers add up to 6 and multiply to 12?

Mathematics
1 answer:
GuDViN [60]3 years ago
7 0
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
x= \frac{-b+/- \sqrt{b^2-4ac} }{2a}

for
x²-6x+12=0
a=1
b=-6
c=12
and remember that √-1=i

x= \frac{-(-6)+/- \sqrt{(-6)^2-4(1)(12)} }{2(1)}
x= \frac{6+/- \sqrt{36-48} }{2}
x= \frac{6+/- \sqrt{-12} }{2}
x= \frac{6+/- (\sqrt{-1})(\sqrt{12}) }{2}
x= \frac{6+/- (i)(2\sqrt{3}) }{2}
x= \frac{6+/- 2i\sqrt{3} }{2}
x=3+/-i√3

the numbers are 3+i√3 and 3-i√3
no real numbers tho
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