Question 01
If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
Given: Mean of a, b, c = M;
ab +bc + ca = 0
Or, (a + b + c)/3 = M
a + b + c = 3M
Squaring both sides, (a + b + c)2 = (3M)2
a2 + b2 + c2 + 2 (ab + bc + ca) = 9M2 Formula used [(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)]
a2 + b2 + c2 + 2. 0 = 9M2 (ab + bc + ca = 0)
(a2 + b2 + c2 )/3 = 3M2 = required mean
Ans. Required mean is 3M2