If the mean of p, q, r is M and pq + qr + rp = 0, then the mean of $p^2, q^2,r^2$ is
Answer & explanation
Correct answer: option 2
(p+q+r)/3 =M
p+q+r = 3M
and, pq + qr + rp = 0
We know (a+b+c)2 = a2+b2+c2 + 2(ab+bc+ca)
(p+q+r)2 = p2+q2+r2 + 2(pq + qr + rp) = p2+q2+r2 (Since pq + qr + rp = 0)
Thus p2+q2+r2 = (p+q+r)2 = 9M2
Mean of p2+q2+r2 = 9M2/3 = 3M2
The correct answer is option (2) : $3M^2$