Question

if x²+x+1=0,then find the value of [x³+1/x³]³

Answer 1

x²+x+1 = 0
⇒  x²+1 = -x
⇒  (x²+1)/x = -1
Now,
   



Put the value of (x²+1)/x from Equn (1) ,

  =(-1)³  [(-1)²-3]³

=  -(-2)³ = 8

Answer 2

x²+x+1 = 0       
multiply with  (1-x)

(1-x)(x²+x+1) = 1 - x³ = 0                 so    x³ = 1 

[ x³ + 1 / x³ ] ³ = [ 1 + 1 ]³ = 8