Odpowiedź:
a₁ = 6
a₂ = x
a₃ = y
a₄ = 48
a₄/a₃ = a₃/a₂ = a₂/a₁
48/y = y/x = x/6 dla x ≠ 0 ∧ y ≠ 0
48/y = y/x
y² = 48x
x² = 6y
y = x²/6
y² = 48x
(x²/6)² = 48x
x⁴/36 = 48x
x⁴ = 48x * 36 = 1728x
x⁴ - 1728x = 0
x(x³ - 1728) = 0
x = 0 ∨ x³ - 1728 = 0
x = 0 ∨ x³ = 1728
x = 0 ∨ x = ∛1728
x = 0 ∨ x = 12
Ponieważ x ≠ 0 więc x = 12
x/6 = y/x
x² = 6y
12² = 6y
144 = 6y
y = 144 : 6 = 24
a₁ = 6 , a₂ = 12 , a₃ = 24 , a₄ = 48
sprawdzenie
a₄/a₃ = a₃/a₂
48/24 = 24/12
2 = 2
L = P
a₃/a₂ = a₂/a₁
24/12 = 12/6
2 = 2
L = P
Odp: x = 12 , y = 24
