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
