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

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

If sqrt(a-x)+sqrt(b-x)+sqrt(c-x)=0 show that (a+b+c+3x)(a+b+c-x)=4(bc+ca+ ab) and if a^((1)/(3))+b^((1)/(3))+c^(-2)=0 then show that (a+b+c)^(3)=27abc

If a^(1/3)+\ b^(1/3)+\ c^(1/3)=0 , then+? (a) a+b+c=0 (b) (a+b+c)^3=27\ a b c (c) a+b+c=3a b c (d) a^3+b^3+c^3=0

If a+ b + c = 0 , show that : a^(3) + b^(3) + c^(3)= 3abc

If a + b + c = 0 , show that a^(3) + b^(3) + c^(3) = 3abc The following are the steps involved in showing the above result. Arrange them in sequential order (A) a^(3) + b^(3) + 3ab (-c) = -c^(3) (B) (a + b)^(3) = (-c)^(3) (C) a + b + c = 0 rArr a + b = -c (D) a^(3) + b^(3) + 3ab (a +b) = -c^(3) (E) a^(3) + b^(3) + c^(2) = 3abc

If a^((1)/(3))+b^((1)/(3))+c^((1)/(3))=0, then+ ?(a)a+b+c=0(b)(a+b+c)^(3)=27abc(c)a+b+c=3abc(d)a^(3)+b^(3)+c^(3)=0

if a, b, c, are all distinct and |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 , show that abc(ab+bc+ca)=a+b+c.

IF |{:(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3):}|=0 , then show that abc=1

If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]| =0, show that abc(ab+bc+ac) = a+b+c