If `a+b+c=0` then prove the following.
`a^(3) +b^(3)+c^(3)=3abc`

If a+b+c=0 then prove the following. a^(5)+b^(5) +c^(5)= -5abc (bc+ca +ab) =(5)/(2) abc (a^(2)+b^(2)+c^(2)) =(5)/(6) (a^(2)+b^(2)+c^(2)) (a^(3) +b^(3) +c^(3))

a ^(3) + b ^(3) - c ^(3) + 3 abc

(a^(3)+b^(3)-c^(3)+3abc)/(a+b-c)=

If a+b+c=5 and ab+bc+ca=10 ,then prove that a^(3)+b^(3)+c^(3)-3abc=-25.

If a+b+c=5 and ab+bc+ca=10, then prove that a^(3)+b^(3)+c^(3)-3abc=-25 .

If a+b+c=0, then which of the following are correct? 1. a^(3) + b^(3) + c^(3) = 3abc 2. a^(2) + b^(2) + c^(2) = -2(ab + bc + ca) 3. a^(3) + b^(3) + c^(3) = -3ab(a+b) Select the correct answer using the code given below

If a+b+c=0 then prove that a^(3)+b^(3)+c^(3)=3abc

If a+b+c= 0 find a^(3) + b^(3) + c^(3) + 3abc

If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 are equal,prove that either a=0 or a^(3)+b^(3)+c^(3)=3abc

If a, b, c are in GP, prove that a^(3), b^(3), c^(3) are in GP.