Question

equação do 2 grau

A)x+y=12
x.y= -35

Answer 1

A)
x + y = 12
x.y = - 35

x = 12 - y
x.y = - 35

x.y = - 35
(12-y).y = - 35
12y - y^2 = - 35
0 = y^2 - 12y - 35
y^2 - 12y - 35 = 0
a= 1; b = - 12; c = - 35
∆= b^2 - 4ac
∆ = (-12)^2 - 4.1.(-35)
∆ = 144 + 140
∆= 284
√∆ = √4.√71
√∆ = 2√71

284: 2
142: 2
71: 71
1

x = [-b +/- √∆]/2a
x = [ - (-12) +/- √284]/2.1
x = [12 + 2√71]/2
x' = 6 + √71
x" = 6 - √71

x = 12 - y
y = 12 - x
y' = 12 - (6 + √71)
y' = 12 - 6 - √71
y' = 6 - √71

y = 12 - x
y = 12 - (6 - √71)
y" = 12 - 6 + √71
y" = 6 + √71

R.:
x" = 6 - √71; y" = 6 + √71
x' = 6 + √71; y' = 6 - √71