# Three members GP

The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.

Correct result:

a =  3
b =  6
c =  12
a2 =  12
b2 =  6
c2 =  3

#### Solution:

Our quadratic equation calculator calculates it.

$b=q_{1} \cdot \ a=2 \cdot \ 3=6$
$c=q_{1} \cdot \ b=2 \cdot \ 6=12$
$a_{2}=21/(1+q_{2}+q_{2}^2)=21/(1+0.5+0.5^2)=12$
$b_{2}=q_{2} \cdot \ a_{2}=0.5 \cdot \ 12=6$
$c_{2}=q_{2} \cdot \ b_{2}=0.5 \cdot \ 6=3$

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