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For any three positive real numbers `a , b` and `c ,9(25 a^2+b^2)+25(c^2-3a c)=15 b(3a+c)dot` Then :

A

a,b and c are in GP

B

b,c and a are in GP

C

b,c and a are in AP

D

a,b and c are in AP

Text Solution

Verified by Experts

The correct Answer is:
C
`(15a)^(2)+(3b)^(2)+(5c)^(2)-45ab-15bc-75ac=0`
`implies (1)/(2){(15a-3b)^(2)+(3b+5c)^(2)+(5c-15a)^(2)}=0`
`implies (15a-3b)^(2)+(3b+5c)^(2)+(5c-15a)^(2)=0`
or `15a-3b=0,3b-5c=0,5c-15a=0`
`:. b=5a,c=3a`
`implies 5a,3a,a` are in AP i.e b,c,a are in AP.
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