Question

Determine a razão da P.G. ( x-1 ; 2x; 4x + 5) com x # 0

Answer 1

P.A = { x + 5, 4.x - 1, x² - 1 }

4.x - 1 = ((x + 5) + (x² - 1)) / 2
2.(4.x - 1) = (x + 5) + (x² - 1)
8.x - 2 = x + 5 + x² - 1
x + 5 + x² - 1 - 8.x + 2 = 0
x² - 7.x + 6 = 0

∆ = (-7)² - 4.(1).(6) = 25

-(-7) ± √∆ / 2.(1)
7 ± √25 / 2
7 ± 5 / 2

x = 6
x = 1