Let `a ,b ,a n dc` be distinct nonzero real numbers such that `(1-a^3)/a=(1-b^3)/b=(1-c^3)/cdot` The value of `(a^3+b3+c^3)` is _____________.

Answer

3

Explanation

Let `(1-a^(3))/(a)=(1-b^(3))/(b)=(1-c^(2))/(c)=k`
`rArr (1-x^(3))/(x)=k`.
where x takes 3 values a, b and c.
`rArr x^(3)+kx-1=0` has roots a, b, c
Now `a + b + c =0" "(1)`
`abc = 1" "(2)`
Hence, `a^(3)+b^(3)+c^(3)=3ab = 3`