Question
If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
Answer: Option A
- We have : a + b + c 3 = M or (a + b + c) = 3M. Now, (a + b + c)M2 = (3M)M2 = 9M2 a2 + b2 + c2 + 2 (ab + bc + ca) = 9M2 a2 + b2 + c2 = 9M2 Required mean = a2 + b2 + c2 3 = 9M2 3 = 3M2
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- We have : a + b + c 3 = M or (a + b + c) = 3M. Now, (a + b + c)M2 = (3M)M2 = 9M2 a2 + b2 + c2 + 2 (ab + bc + ca) = 9M2 a2 + b2 + c2 = 9M2 Required mean = a2 + b2 + c2 3 = 9M2 3 = 3M2
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