Question

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

Answer 1

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