Question

Aflati b1 si q din urmatoarele relatii ale progresiei geometrice:

b5-b1=80, b4-b2=24, b1=?, q=?

Answer 1

Răspuns:

Explicație pas cu pas:

b1*q^4 - b1 = 80

b1*q^3 - b1*q = 24

b1*(q^4 - 1) = 80

b1*(q^2 - 1)*(q^2 + 1) = 80

b1*q*(q^2 - 1) = 24

b1*(q^2 - 1) = 24/q

(q^2 + 1)*24/q = 80

24*(q^2 + 1) = 80q

24q^2 - 80q + 24 = 0

3q^2 - 10q + 3 = 0

Δ = 100 - 36 = 64

q1 = (10 + 8)/6 = 18/6 = 3

q2 = (10 - 8)/6 = 2/6 = 1/3

_______

q = 3

b1*(81 - 1) = 80 ⇒ b1*80 = 80 ⇒ b1 = 1

_______

q = 1/3

b1*(1/81 - 1) = 80 ⇒ b1*(-80/81) = 80 ⇒ b1 = -80*81/80 = -81