If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2+b2+c23 is :

We have : ( a + b + c) / 3 = M   or (a + b + c) = 3M.

Now.  $a+b+c2=3M2=9M2$ .

$<=>a2+b2+c2+2ab+bc+ca=9M2$

$a2+b2+c2=9M2 ,(ab+bc+ca=0)$     

Required mean = $\frac{a2+b2+c2}{3}=\frac{9M2}{3}=3M2$ .