Discussion

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

Answer: B

Given \(\frac{a+b+c}{3} = M \Rightarrow a+b+c=3M\).

We know the algebraic identity: \((a+b+c)^2 = a^2+b^2+c^2 + 2(ab+bc+ca)\).

Substitute the given values:

\((3M)^2 = (a^2+b^2+c^2) + 2(0)\)

\(9M^2 = a^2+b^2+c^2\).

The mean of a², b², c² is \(\frac{a^2+b^2+c^2}{3} = \frac{9M^2}{3} = 3M^2\).

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