Question

{x+y=2
4xy=3

Resolver com baskara

Answer 1

x + y = 2
4xy = 3

x + y = 2
y = 2 - x

4xy = 3
4x(2 - x) = 3
8x - 4x² = 3
- 4x² + 8x - 3 = 0
a = - 4, b = 8, c = - 3

Δ = b² - 4ac
Δ = 8² - 4 (- 4) (- 3)
Δ = 64 - 48
Δ = 16
Δ = 4²

x = (- b ± √Δ)/2a
x = (- 8 ± √4²)/2 . (- 4)
x = (- 8 ± 4)/- 8
x = (8 ± 4)/8

x' = (8 + 4)/8 = 12/8 = 3/2
x'' = (8 - 4)/8 = 4/8 = 1/2

y' = 2 - x'
y' = 2 - 3/2
y' = (- 3 + 4)/2
y' = 1/2

y'' = 2 - x''
y'' = 2 - 1/2
y'' = (- 1 + 4)/2
y'' = 3/2


x' = 3/2      y' = 1/2
x'' = 1/2     y'' = 3/2