if a+b+c=0 then a²÷bc+b²÷ca+c²÷ab
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a+b+c=0
a+b=-c. …………….(1)
On cubing both sides
a^3+b^3+3a.b(a+b)=-c^3
a^3+b^3+c^3+3a.b(-c)=0
a^3+b^3+c^3=3a.b.c
Divide both side by a.b c
a^2/b.c+b^2/c.a+c^2/a.b=3
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