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

 

Hi!

 

Let the three numbers in G.P. be a, ar and ar2.
a + ar + ar2 = 21         (Given)
 a2( 1+ r + r2)2 = 441      ... (1)
 
(a)2 + (ar)2 + (ar2)2 = 189        (Given)
a2 (1 + r2 + r4) = 189     ...  (2)
 
From (1) and (2), we get
 
Thus, the three numbers in G.P. are 3, 6 and 12.

Cheers!

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