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Q.
If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2+b2+c2/3 is :
A.
M
B.
3 M^2
C.
2 (M/3)
D.
M^2
View Answer
Correct choice: B
Explanation:
We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. (a+b+c)2=(3M)2=9M2 <=>a2+b2+c2+2(ab+bc+ca)=9M2 a2+b2+c2=9M2 ,(ab+bc+ca=0) Required mean =(a2+b2+c2/3)=9M2/3=3M2 .
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