Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The sum of the squares of three distinct real number which are in G.P. is S 2 . If their sum is α S then α 2 belongs to -
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
Let 
, a , ar, three terms in G.P.
given a 2 
= s 2 ….(1)
and a 
= α s ….(2)
divide (1) by (2)
= 
= 
….(3)
from (2) & (3)
a = 
put in equation (1)
⇒ 
= 
⇒ 
> 3 ⇒ 3 α 4 – 10 α 2 + 3 < 0
⇒ (3 α 2 – 1) ( α 2 – 3) < 0
⇒ 
< α 2 < 3 , [ α 2 ≠ 1 we get a = 0]
α 2 ∈ 
∪ (1, 3).
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