Question

Calcule o valor de X de acordo com o Teorema de Tales.

Answer 1

$\frac{2x + 2}{6x} = \frac{2x + 4}{2x + 12}$
6x . (2x + 4) = (2x + 2). (2x + 12)
12x² + 24x = 4x² + 24x + 4x + 24
12x² - 4x² + 24x - 24x - 4x - 24 = 0
8x² - 4x - 24 = 0    ÷ 4
2x² - x - 6 = 0
Δ = (-1)² - 4 . 2 . (-6)
Δ = 1 + 48
Δ = 49        >>   √Δ = 7

x₁ = $\frac{1 + 7}{4} = \frac{8}{4} = 2$
x₂ = $\frac{1 - 7}{4} = \frac{-6}{4} = \frac{-3}{2}$ (Não convém)

Resposta x = 2


b) $\frac{2x + 2}{2} = \frac{2x + 6 }{3}$
3.(2x + 2) = 2.(2x + 6)
6x + 6 = 4x + 12
6x - 4x = 12 - 6
2x = 6
x = 6/2
x = 3