SOLUTION: The sum of three numbers in G.P is 21 and the sum of their squares is 189.Find the numbers

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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