Question

x+y=4 e x ao quadrado-xy=seis

Answer 1

x + y = 4

x² - xy = 6

x = 4 - y

x² - xy = 6
x(x - y) = 6

(4 - y).(4 - y - y) = 6
(4 - y).(4 - 2y) = 6
16 - 8y - 4y + 2y² = 6
16 - 6 - 12y + 2y² = 0
10 - 12y + 2y² = 0

2y² - 12y + 10 = 0 (:2)
y² - 6y + 5 = 0

a = 1
b = - 6
c = 5

Δ = b² - 4ac
Δ = (-6)² - 4.1.5
Δ = 36 - 20
Δ = 16

y = - b +/- √Δ = - (-6) +/- √16
           2a               2.1

y' = 6 + 4 = 10/2 = 5
         2

y" = 6 - 4 = 2/2 = 1
        2

y = 5 e y = 1
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Quando:

y = 5
x + y = 4
x + 5 = 4
x = 4 - 5
x = - 1

Quando:

y = 1
x + y = 4
x + 1 = 4
x = 4 - 1
x = 3
_______________________
Resp.: 
x = - 1 y = 5
ou
x = 3 y = 1
__________________________

x² - xy = 6
3² - 3.1 = 6
9 - 3 = 6

x² - xy = 6
(-1)² - (-1).5 = 6
1 + 5 = 6