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If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2+b2+c23 is :

Correct Answer: 3 M^2

Explanation:

We have : ( a + b + c) / 3 = M   or (a + b + c) = 3M.


Now.  a + b + c 2 = 3 M 2 = 9 M 2  .


 


 


 


< = > a 2 + b 2 + c 2 + 2 a b + b c + c a = 9 M 2


 


 


 


a 2 + b 2 + c 2 = 9 M 2       , ( a b + b c + c a = 0 )      


 


 


 


Required mean = a 2 + b 2 + c 2 3 = 9 M 2 3 = 3 M 2  .


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