show that x^(a^2)*(b^-1)*(c^-1) * x^(a^-1)*(b^2)*(c^-1) * x^(a^-1)*(b^-1)*(c^2)=x^3 if a+b+c=0
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x^(a²/bc) .x^(b²/ca).x^(c²/ab) =x³
x^(a²/bc + b²/ca +c²/ab) = x³
x^(a³/abc + b³/abc +c³/abc ) =x³
x^{(a³+b³+c³)/abc} = x³
(a³ + b³ + c³)/3abc = 3
a³ + b³ + c³ = 3abc
but this is possible only when ,
a + b + c =0
x^(a²/bc + b²/ca +c²/ab) = x³
x^(a³/abc + b³/abc +c³/abc ) =x³
x^{(a³+b³+c³)/abc} = x³
(a³ + b³ + c³)/3abc = 3
a³ + b³ + c³ = 3abc
but this is possible only when ,
a + b + c =0
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