If `1/a+1/b+1/c=1/(a+b+c)` then show that `1/a^3+1/b^3+1/c^3=1/(a^3+b^3+c^3)`

If a^(1//3)+b^(1//3)+c^(1//3)=0 , then show that (a+b+c)^(3)=27 abc .

If a^(1//3)+b^(1//3)+c^(1//3)=0 , then :

If a ^(1//3) + b ^(1//3) + c ^(1//3) = 0, then the value of (a + b + c) ^(3) will be:

By using properties of determinants. Show that: (i) |1a a^2 1bb^2 1cc^2|=(a-b)(b-c)(c-a) (ii) |1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a)(a+b+c)