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

Since the mean of $a, b, c$ is $M$, $a + b + c = 3M$. Given $ab + bc + ca = 0$, $a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + bc + ca) = 9M^2$. Thus the mean of $a^2, b^2, c^2$ is $\frac{9M^2}{3} = 3M^2$.