" 2."a^(3)+b^(3)+c^(3)-3abc

If c be a whole number , but not a natural number and if (a^(2))/(b)+(b^(2))/(a)=3c " then find " (a^(3)+b^(3)+c^(3)-3abc).

If a=-1,b=2,c=3," then"(a^(3)+b^(3)+c^(3)-3abc)/((a-b)^(2)+(b-c)^(2)+(c-a)^(2))=

Let a=Sigma_(n=0)^(oo) (x^(3n))/((3n))!, b =Sigma_(n=1)^(oo) (x^(3n-2))/(3n-2)! and C=Sigma_(n=1)^(oo) (x^(3n-1))/(3n-1)! and w be a complex cube root of unity Statement 1: a+b+c =e^(x),a+bw+cw^(2)=e^(wx) and a+bw^(2)+cw=e^(w^(2)) Statement 2: a^(3)+b^(3)+C^(3)-3abc=1

Let a=Sigma_(n=0)^(oo) (x^(3n))/((3n))!, b =Sigma_(n=1)^(oo) (x^(3n-2))/(3n-2)! and C=Sigma_(n=1)^(oo) (x^(3n-1))/(3n-1)! and w be a complex cube root of unity Statement 1: a+b+c =e^(x),a+bw+cw^(2)=e^(wx) and a+bw^(2)+cw=e^(w^(2)) Statement 2: a^(3)+b^(3)+C^(3)-3abc=1

Prove that a^(3)+b^(3)+c^(3)-3abc=(1)/(2)(a+b+c){(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}

Prove that: a^(3)+b^(3)+c^(3)-3abc=(1)/(2)(a+b+c){a-b)^(2)+(b-c)^(2)+(c-a)^(2)}

Verify : a^(3)+b^(3)+c^(3)-3abc=(1)/(2)(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]

Prove: a^(3)+b^(3)+c^(3)-3abc=(1)/(2)(a+b+c){(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}