Question

Resolva a Equaçao

a) x²=x+1

b) (x-2)² + (x+1)²=5

Answer 1

b)
(x - 2)² + (x + 1)² = 5
x² - 2.2x + 4 + x² + 2x + 1 = 5
x² - 4x + 4 + x² + 2x + 1 - 5 = 0
x² + x² - 4x + 2x + 4 - 4 = 0

2x² - 2x = 0
x(2x - 2) = 0

x = 0
ou
2x - 2 = 0
2x = 2
x = 2/2
x = 1

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a)

x² = x + 1
x² - x - 1 = 0

a = 1; b = - 1; c = - 1

Δ = b² - 4ac
Δ = (-1)² - 4.1.(-1)
Δ = 1 + 4
Δ = 5

x = - b +/- √Δ = - (-1) +/- √5
           2a              2.1

x' = 1 +√5
        2

x" = 1 - √5
         2