x+y=11/12
xy=1/6
x+y=11/12
minus x both sides
y=11/12-x
sub that for y
x(11/12-x)=1/6
11/12x-x^2=1/6
times -1
x^2-11/12x=-1/6
add 1/6 both sides
x^2-11/12x+1/6=0
use quadratic formula
for
ax^2+bx+c=0
x=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
a=1
b=-11/12
c=1/6
x=[tex] \frac{-(-11/12)+/- \sqrt{(-11/12)^2-4(1)(1/6)} }{2(1)} [/tex]
x=[tex] \frac{11/12+/- \sqrt{(121/144)-(4/6)} }{2} [/tex]
x=[tex] \frac{11/12+/- \sqrt{(121/144)-(2/3)} }{2} [/tex]
x=[tex] \frac{11/12+/- \sqrt{(121/144)-(96/144)} }{2} [/tex]
x=[tex] \frac{11/12+/- \sqrt{25/144} }{2} [/tex]
x=[tex] \frac{11/12+/- (5/12)}{2} [/tex]
x=(11/24)+/-(5/24)
x=(11+/-5)/24
x=(16/24) or (6/24)
x=(2/3) or (1/4)
the numbers are 2/3 and 1/4
2/3*1/4=2/12=1/6
2/3+1/4=8/12+3/12=11/12
the smaller number is 3/12 or 1/4
smaller number is 1/4
