If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
Choose the most appropriate option.
A) M2  B) 3M2  C) 6M2  D) 9M2  E) None of these
Explanation :   We have : (a + b + c)/3 = M or (a + b + c) = 3M.   Now, (a + b + c)*(a + b + c) = (3M)^2 = 9M^2   a2 + b2 + c2 + 2 (ab + bc + ca) = 9M^2   a2 + b2 + c2 = 9M^2   Required mean = (a2 + b2 + c2)/3 = 9M^2/3 = 3M2   Answer : 3M2
<result>B</result>
If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is: