question_answer 75)

If a, b and c are real numbers, and =0 show that either a+b+c=0 or a=b=c.  

Answer:

      Operate  we get             Take 2(a + b + c) as common             Operate             Expand along C1                 .                   = 2(a + b + c) . [(b ? c) (c ? b) ? (b ? a) (c ? a)]             = 2(a + b + c) . [? (b ? c)2 ? (bc ? ab ? ac + a2)]             = 2 (a + b + c) [?b2 ? c2 + 2bc ? bc + ab + ac ? a2]             = ?2 (a + b + c) (a2 + b2 + c2 ? ab ? bc ? ca)             = ? (a + b + c) (2a2 + 2b2 + 2c2 ? 2ab ? 2bc ? 2ca)       = ? (a + b + c) (a2 + b2 ? 2ab + b2 + c2 ? 2bc + c2                   + a2 ? 2ca)                    Given