Question

20PONTOOOOOOOOOS! $\frac{x^2-2x}{4} = \frac{1}{4} + \frac{x}{2}$

Answer 1

(x² - 2.x)/4 - 1/4 = x/2
(x² - 2.x - 1)/4 = x/2
2.(x² - 2.x - 1) = 4.x
2.x² - 4.x - 2 - 4.x = 0
2.x² - 8.x - 2 = 0 (divide por 2 ambos os membros)
x² - 4.x - 1 = 0

Δ = (-4)² - 4.1.(-1) = 16 + 4 = 20

x' = (4 + √20)/2 = (4 + 2.√5) / 2 = 2.(2 + √5) / 2 = 2 + √5
x'' = (4 - √20)/2 = (4 - 2.√5) / 2 = 2.(2 - √5) / 2 = 2 - √5