Respostas

2014-08-27T21:03:25-03:00
 \left \{ {{x - y = 9} \atop {x.y=-14}} \right.  \\  \\ x = 9+ y \\  \\ x . y = - 14 \\ (9+y).y=-14 \\ 9y +  y^{2} = - 14 \\  y^{2} + 9y + 14 = 0 \\  \\ \Delta = b^{2} - 4 . a . c \\ \Delta = (9)^{2}  - 4 . (1) . (14) \\ \Delta = 81 - 56 \\ \Delta = 25

y =  \frac{- b \±  \sqrt{\Delta}}{2a} \\  \\ y =  \frac{- 9 \± \sqrt{25}}{2.1}  \\  \\ y =  \frac{-9 \± 5}{2}  \\  \\ y' =  \frac{- 9 - 5}{2} =  \frac{-14}{2} = - 7 \\  \\ y'' =  \frac{- 9 + 5}{2} =  \frac{- 4}{2} = - 2


Valor de x quando y = -2

x - y = 9 \\ x - (-2) = 9 \\ x + 2 = 9 \\ x = 9 +2 \\ x = 11

Valor de x quando y = - 7

x - y = 9 \\ x - (- 7) = 9 \\ x + 7 = 9 \\ x = 9 - 7 \\ x = 2


Solução: x = 2 quando y = - 7x = 11 quando y = - 2.
1 5 1