If the mean of a, b, c is M and \(ab+bc+ca=0\), then the mean of \(a^2, b^2\) and \(c^2\) will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(3M^2\)
The sum of the squares comes from the identity \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\), in which the given \(ab+bc+ca=0\) drops out.
The mean of a, b, c is M, so \(a+b+c=3M\)
\(a^2+b^2+c^2=(3M)^2-2\times0=9M^2\)
Mean of \(a^2\), \(b^2\), \(c^2\): \(\frac{9M^2}{3}=3M^2\)