If mean of a, b, c is M and a b+b c+c a=0, then mean of a^{2}, b^{2}, c^{2} is

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If the mean of $a, b, c$ is $M$ and $a b+b c+c a=0,$ then the mean of $a^{2}, b^{2}, c^{2}$ is

A

$M ^{2}$

B

$3 M ^{2}$

C

$6 M ^{2}$

D

$9 M ^{2}$

Solution

Given $\frac{a+b+c}{3}=M$

or $(a+b+c)=3 M$

$(a+b+c)^{2}=9 M^{2}$

i.e. $a^{2}+b^{2}+c^{2}+2(a b+b c+c a)=9 M^{2}$

$a b+b c+c a =0$

$a^{2}+b^{2}+c^{2} =9 M^{2}$

Standard 13

Quantitative Aptitude

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