If 3 (a^{2} + b^{2} + c^{2} ) = (a + b + c)^{2} , then the relation between a, b and c is
Given , 3 (a^{2} + b^{2} + c^{2} ) = (a + b + c)^{2}
3 (a^{2} + b^{2} + c^{2} )=3 (a^{2} + b^{2} + c^{2}) +2[ab+bc+ca]
2 (a^{2} + b^{2} + c^{2} )= +2[ab+bc+ca]
(a^{2} + b^{2} + c^{2} )= [ab+bc+ca]
(a^{2} -ab) + (b^{2} -bc) + (c^{2} -ca) = 0
a(a-b) + b(b-c) + c(c-a) = 0
This is only possible when a=b=c .
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