SOLUTION: find the possible values of p if p-3,3p-5,18-5 are consecutive terms of a geometric progression.

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Question 1152960: find the possible values of p if p-3,3p-5,18-5 are consecutive terms of a geometric progression.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


consecutive terms of a geometric progression
p-3,3p-5,18-5....not sure about third term, I guess you have 18p-5

first express common ratio using given terms:
r=%283p-5%29%2F%28p-3%29
r=%2818p-5%29%2F%283p-5%29
r=r=>
%283p-5%29%2F%28p-3%29=%2818p-5%29%2F%283p-5%29
%283p-5%29%283p-5%29=%2818p-5%29%28p-3%29
9p%5E2-30p+%2B+25=18p%5E2-+59p+%2B+15
18p%5E2+-+59p+%2B+15-9p%5E2+%2B+30p+-25=0
9p%5E2+-+29p+-+10=0
use quadratic formula
p=%28-%28-29%29%2B-sqrt%28%28-29%29%5E2-4%2A9%2A%28-10%29%29%2F%282%2A9%29%29
p=%2829%2B-sqrt%28841%2B360%29%29%2F18
p=%2829%2B-sqrt%281201%29%29%2F18

exact solutions:
p=%2829%2Bsqrt%281201%29%29%2F18 or
p=%2829-sqrt%281201%29%29%2F18


Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

My point is that there is no any sense to solve the problem where the input data is unclear.

The only right way in this case (in such cases) is to point to the visitor that his or her data is defective.