Question 24

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

Solution

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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