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  1. If   a + b + c = m and
    1
    +
    1
    +
    1
    = 0, then average of a2,b2 and c2 is
    abc
    1. m2
    2. m2
      3
    3. m2
      9
    4. m2
      27
Correct Option: B

a + b + c = m

and ,
1
+
1
+
1
= 0
abc

⇒ 
bc + ac + ab
= 0
abc

⇒  bc + ac + ab = 0
∴  (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒  m2 = a2 + b2 + c2 + 2 × 0
⇒  a2 + b2 + c2 = m2
∴  Required average =
a2 + b2 + c2
=
m2
33



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