Odpowiedź:
zad 5
a₁ = 81
a₂ = a₁q = - 27
a₃ = a₁q² = 9
a₃/a₂ = a₂/a₁ = q
9/(- 27) = (-27)/81 = - 1/3
a₆ = a₁q⁵ = 81 * (- 1/3)⁵ = 81 * (- 1/243) = - 81/243 = - 1/3
zad 6
a₁ = 4
a₂ = x - 5
a₃ = 36
a₃/a₂ = a₂/a₁ = q
a₂² = a₃ * a₁
(x - 5)² = 36 * 4 = 144
x² - 10x + 25 = 144
x² - 10x + 25 - 144 = 0
x² - 10x - 119 = 0
a = 1 , b = - 10 , c = - 119
Δ = b² - 4ac = (- 10)² - 4 * 1 * (- 119) = 100 + 476 = 576
√Δ = √576 = 24
x₁ = (- b - √Δ)/2a = (10 - 24)/2 = - 14/2 = - 7
x₂ = ( - b + √Δ)/2a = (10 + 24)/2 = 34/2 = 17
