If the mean of \(a\), \(b\), and \(c\) is \(M\); \(ab + bc + ca = 0\); and the mean of \(a^2\), \(b^2\) and \(c^2\) is \(KM^2\), then \(K\) is equal to

Question and options

If the mean of

a

b

, and

c

M

;

ab + bc + ca = 0

; and the mean of

a^2

b^2

and

c^2

KM^2

, then

K

is equal to

Correct answer: A - 3

a^2+b^2+c^2 = (a+b+c)^2 - 2(ab+bc+ca) = (3M)^2 = 9M^2. Mean = 3M^2, so K = 3.