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 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

If a+b+c=0 and a^2+b^2+c^2=1, then (a) a b+b c+c a=1/2 (b) a b+b c+c a=-1/2 (c) a^4+b^4+c^4=1/2 (d) a^4+b^4+c^4=3/2

If a b c = 0, then ({(x^a)^b}^c)/({(x^b)^c}^a) = (a)3 (b) 0 (c) -1 (d) 1

Prove: |[b+c ,a-b ,a], [c+a, b-c ,b], [a+b, c-a, c]|=3a b c-a^3-b^3-c^3

If a+b+c=0, then a^(3)+b^(3)+c^(3) is equal to

If a/b+b/a=\ -1, then a^3-b^3=? (a)1 (b) -1 (c) 1/2 (d) 0

If the points ((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),((b^2-3)/((b-1))) , ((c^3)/(c-1)) and (((c^2-3))/((c-1))), where a , b , c are different from 1, lie on the l x+m y+n=0 , then (a) a+b+c=-m/l (b) a b+b c+c a=n/l (c) a b c=((m+n))/l (d) a b c-(b c+c a+a b)+3(a+b+c)=0

If a/b+b/a=1, then a^3+b^3=? (a) 1 (b) -1 (c) 1/2 (d) 0

If a , b ,c in Ra n da(a+b)+b(b+c)+c(c+a)=0 then a. a=b=c=0 b. a+b+c+=0 c. (a-b)^2+(b-c)^2+(c-a)^2=0 d. a^3+b^3+c^3+3a b c=0

Prove: \ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c