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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
It is given that $$ab+bc+ca=0$$
The mean of $$a^{2}$$, $$b^{2}$$ and $$c^{2}$$ is $$KM^{2}$$
$$a^2+b^2+c^2=3kM^2$$
The mean of a, b and c is $$M$$.
$$a+b+c=3M$$
Squaring both sides -
$$a^2+b^2+c^2+2(ab+bc+ca)=9M^2$$
$$3kM^2+2(0)=9M^2$$
$$k=3$$
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