Question

-x ao quadrado +x+1=0

Answer 1

-x² + x + 1 = 0

Multiplica por -1 para facilitar os cálculos:

-x² + x + 1 = 0 ( - 1 )

x² - x - 1 = 0

Δ = b² − 4ac

Δ = (−1)² −4⋅(1)⋅(−1)

Δ = 1 + 4

Δ = 5

$x = \dfrac{-b \pm \sqrt{\Delta}}{2 . a}\\ \\ \\ x = \dfrac{-(-1) \pm \sqrt{5}}{2 . 1}\\ \\ \\ x = \dfrac{1 \pm \sqrt{5}}{2}\\ \\ \\ x' = \dfrac{1 - \sqrt{5}}{2}\\ \\ \\ x'' = \dfrac{1 + \sqrt{5}}{2}$

S = {$\dfrac{1 - \sqrt{5}}{2} \ , \ \ \dfrac{1 + \sqrt{5}}{2}$}