Odpowiedzi

Najlepsza Odpowiedź!
2009-11-16T15:37:49+01:00
X² - 65x + 1050,5 =0,5
x² -65x + 1050 = 0
Δ = 4225 - 4200 =25
√Δ = 5
x₁ = 65-5 / 2 = 60/2 =30
x₂ =65+5 /2 = 70/2 =35

a₁ + a₄ =35
a₂ +a₃ =30

a₁
a₂ = a₁ * q
a₃ = a₂ * q = a₁ *q²
a₄ = a1 * q³


a₁ + a₁ * q³ = 35 => a₁(1+q³) = 35 => a₁ = 35 / 1+q³
a₁ * q + a₁ *q² = 30

35 / 1+q³ * q + 35 / 1+q³ * q² =30

(35q + 35q²) : (1+q³) = 30
35(1+q) / (1+q)(1-q+q²) = 30
35q / 1-q+q² =30
30q² -30q + 30 = 35q
30q² -65q +30 = 0 /:5
6q² -13q + 6 = 0
Δ =169-144=25
√Δ =5
q₁ = 13-5 / 12 = 8/12 = 2/3
q₂ = 18/12 = 3/2

1⁰ dla q = 2/3

a₁=35 / 1 + (2/3)³= 35 / 1 + 8/27 = 35/ 35/27 = 27
a₂=27 * 2/3 = 18
a₃=18 * 2/3 = 12
a₄ =12 * 2/3 = 8

2⁰ dla q = 3/2

a₁= 35/ 1 + (3/2)³ = 35/ 1+27/8 = 35/(35/8) = 35 * 8/35 =8
a₂=8 * 3/2 =12
a₃ =18
a₄=27

odp: Te liczby to 8,12,18,27.