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

Option 1)
M²
Option 2)
3M²
Option 3)
6M²
Option 4)
2M²
Option 5)
9M²

Answers (1)

R rishi raj

$\frac{(a+b+c)}{3} = m$
$=> a+b+c= 3m$
$ab+bc+ca=0$
$As (a+b+c)^{2} = a^{2}+b^{2}+c^{2} + 2(ab+bc+ac)$
$=> (3m)^{2} = (a^{2}+b^{2}+c^{2} )+ 2(0)$
$=> a^{2}+b^{2}+c^{2} = 9m^{2}$
$Avg. \: O\! f (a^{2}+b^{2}+c^{2} ) is = (9m^{2}/3)$
$= 3m^{2}$