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

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

If a+b+c=1,a^(2)+b^(2)+c^(2)=9 and a^(3)+b^(3)+c^(3)=1, then (1)/(a)+(1)/(b)+(1)/(c) is (i)0 (ii) -1(iii)1(iv)3

If (3a+1)^(2) +(b-1)^(2) +(2c-3)^(2)=0 , then value of (3a+b+2c) is

In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0), then centroid of A B C) is (1/2,2/3) (b) (1/3,2/3) (2/3,1) (d) none of these

Prove that : tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0

Prove that : tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0

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 different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(2),c^(3)-1)|=0 then