If a2 + b2 + c2 - ab-bc - ca = 0, p...
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If a2 + b2 + c2 - ab-bc - ca = 0, prove that a ca= 0, prove that a = b = c.

SSC CGL
Maths
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( a^{2}+b^{2}+c^{2}-a b-b c-c a=0-0 ) We know that ( a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c)left(a^{2}+b^{2}+c^{2}-a b-b c-c aright) ) From eq ( a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c) times(0) ) ( a^{3}+b^{3}+c^{3}-3 a b c=0 ) ( a^{3}+b^{3}+c^{3}=3 a b c ) let ( a-b=c quad 80 ) ( a^{3}+a^{3}+a^{3}=3 a^{3} ) ( Rightarrow quad 3 a^{3}=3 a^{3} quad s_{0}, quad mid L H_{s}=R H S )
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