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)

\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}

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