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

Answer: Option B

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
$$\begin{array}{rl}& =\left(\frac{a^2+b^2+c^2}{3}\right)\\ & =\frac{9M^2}{3}\\ & =3M^2\end{array}$$