factor -47
it's prime
we have to use quadratic
so
set equations
x+y=18
xy=-47
x+y=18
minus x from both sides
y=18-x
sub 18-x for y in other equatin
x(18-x)=-47
distribute
18x-x^2=-47
times both sides by -1
x^2-18x=47
minus 47 from both sides
1x^2-18x-47=0
for equation
ax^2+bx+c=0
x=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
a=1
b=-18
c=-47
x=[tex] \frac{-(-18)+/- \sqrt{(-18)^2-4(1)(-47)} }{2(1)} [/tex]
x=[tex] \frac{18+/- \sqrt{324+188} }{2} [/tex]
x=[tex] \frac{18+/- 16\sqrt{2} }{2} [/tex]
x=9+/-8√2
the numbers are
9+8√2 and 9-8√2
