Question

A, b, c, d sunt in progresie geometrica
d-a=7
c-b=2
Aflati ratia.

Answer 1

d - a = 7

c - b = 2


b = a • q

c = a • q^2

d = a • q^3


aq^3 - a = 7

a • q^2 = a • q = 2 =>


a (q^3 - 1) = 7

a • q^2 - a • q = 2 =>


a (q - 1) (q^2 + q + 1) = 7

a • q (q - 1) = 2 =>


a (q - 1) (q^2 + q + 1) = 7 / a ( q - 1) = 2/q =>


2q^2 - 5q + 2 = 0 => D = 25 - 16 = 9


Q112 = 5 +_ 3 / 4 =>


Q1 = 2

Q2 = 1/2


Succes.