A=(a^2 ab ac Ab b^2 BC Ac BC c^2) then a^2+b^2+c^2=1 then A^2=?
Lakshmi , 8 Years ago
Grade 12th pass
Magical Mathematics[Interesting Approach]> A=(a^2 ab ac Ab b^2 BC Ac BC c^2) then a^...
1 AnswersVikas TU
A2= a4+a2b2+a2c2+a3b+ab3+abc2+a3c+ab2c+ac3+a3b+ab3+abc2+a2b2+b4+b2c2+a2bc+b3c+a3c+ab2c+ac3+a2bc+b3c+bc3+a2c2+b2c2+c4
=a2(a2+b2+c2)+a3b+ab3+abc2+a3c+ab2c+ac3+a3b+ab3+abc2+b2(a2+b2+c2)+a2bc+b3c+a3c+ab2c+ac3+a2bc+b3c+bc3+c2(a2+b2+c2)
We know that a2+b2+c2=1 from the identitiy.
=a2+a3b+ab3+abc2+a3c+ab2c+ac3+a3b+ab3+abc2+b2+a2bc+b3c+a3c+ab2c+ac3+a2bc+b3c+bc3+c2
=1+a3b+ab3+abc2+a3c+ab2c+ac3+a3b+ab3+abc2+a2bc+b3c+a3c+ab2c+ac3+a2bc+b3c+bc3
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