Question 1135338: The sum of three numbers in G.P is 21 and the sum of their squares is 189.Find the numbers
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
In General we write a Geometric Sequence like this:
{  ,  ,  ,  , ... } where:
is the first term, and
 is the factor between the terms (called the "common ratio")
if the sum of three numbers in G.P is  , we have
 ....solve for
 .....eq.1
and, if the sum of their squares is  , we have
 ...solve for
 ........eq.2
from eq.1 and eq.2 we have
 ........square both sides
 .........factor
solutions:
if  =>
if  =>
if  => use quadratic formula and you will get complex solutions
 ->disregard
now find :
.....eq.1, plug in
or
.....eq.1, plug in
then , , will be
if and
or
if and
you actually got same terms in reverse order
check their sum:
 and
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