If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $ a^2+b^2+c^2 3$ is :

গ) $3M^2$ — We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. $ (a+b+c )^2= (3M )^2=9M^2$ $ a^2+b^2+c^2+2 (ab+bc+ca )=9M^2$ $a^2+b^2+c^2=9M^ 2\;\;\; ,(ab+bc+ca=0)$ Required mean = $ ( a^2+b^2+c^2 3 )= 9M^2 3=3M^2$

If the mean of a, b, c is M and ab + bc +… | Answer

Subject

Quantitative Aptitude

Topic

Average

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^2+b^2+c^2}3$ is :
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ক)

খ)

গ)

$3M^2$

ঘ)

$M^2$

Explanation

We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now.

\left(a+b+c\right)^2=\left(3M\right)^2=9M^2

<=>a^2+b^2+c^2+2\left(ab+bc+ca\right)=9M^2

a^2+b^2+c^2=9M^{2\;\;\;},(ab+bc+ca=0)

Required mean =

\left(\frac{a^2+b^2+c^2}3\right)=\frac{9M^2}3=3M^2

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If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2+b2+c23\frac{a^2+b^2+c^2}33a2+b2+c2​ is :Reading

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2+b2+c23\frac{a^2+b^2+c^2}33a2+b2+c2​ is :

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If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^2+b^2+c^2}3$ is :
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If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^2+b^2+c^2}3$ is :