Jul 22, 2015

Express the following as a sum of perfect square | 16a2 + b2 + 9c2 - 4ab - 3bc - 12ca

  Express the following as a sum of perfect square:
    16a2 + b2 + 9c2 - 4ab - 3bc - 12ca

=1/2.(2.16a2 + 2. b2 + 2. 9c2 - 8ab - 6bc - 24ca)
= 1/2.(16a2 + 16a2+ b2 + b2 + 9c2 + 9c2 - 8ab - 6bc - 24ca)
= 1/2.(16a2 - 8ab + b2 + b2 - 6bc + 9c2 + 16a2 - 24ca + 9c2)
= 1/2.{(16a2 - 8ab + b2 ) + ( b2 - 6bc + 9c2) + ( 16a2 - 24ca + 9c2)}
= 1/2.{(16a2 - 2.4a.b + b2 ) + ( b2 - 2.b.3c + 9c2) + ( 16a2 - 2.4a.3c + 9c2)}
= 1/2.{(4a - b)2 + ( b-3c )2 + ( 4a-3c )2} Answer


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