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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 ,b`and`c`are in`AdotPdot`(2) `a ,b`and `c`are in `GdotPdot``b ,c`and `a`are in `GdotPdot`(4) `b , c`and `a`are in `AdotPdot`A. a,b and c are in GPB. b,c and a are in GPC. b,c and a are in APD. a,b and c are in AP |
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Answer» Correct Answer - 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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