If the mean of a, b, c, is M and ab + bc + ca = 0, then the mean of a², b², c² is -

A. M²

B. 3M²

C. 6M²

D. 9M²

Answer: Option B

Solution(By Examveda Team)

We have :
$$\frac{a + b + c}{3}$$   = 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
[$$\because $$ (ab + bc + ca) = 0]
∴ Required mean
$$\eqalign{ & = \left( {\frac{{{a^2} + {b^2} + {c^2}}}{3}} \right) \cr & = \frac{{9{M^2}}}{3} \cr & = 3{M^2} \cr} $$