Question

prove that x³-1=(x-1)(x²+x+1).

Hey guys please answer this question........​

Answer 1

X² + x + 1 = 0

⇒ x² + x + 1 -x = 0 - x

⇒x² + 1 = -x

⇒(x² + 1)/x = -x/x

⇒ x + 1/x = -1

Using a³+b³ = (a+b)³ - 3ab(a+b)

x³ + 1/x³ = (x+1/x)³ - 3×x×1/x×(x+1/x)

Thus (x³ + 1/x³)³ = [(x+1/x)³ - 3×x×1/x×(x+1/x)]³

=[ (-1)³ - 3×(x×1/x)×(-1) ]³

=[ (-1)³ - 3×(1)×(-1) ]³

=[ -1 -3×(-1) ]³

=[ -1 + 3 ]³

=[2]³

=8

Answer 2

Answer:

LHS

x³ -1

= x³ -1³

= (x -1)(x² + 1² +x.1)

= (x -1)(x² +x +1)

formula

' a³ - b³ = (a - b)(a² + b ² +ab)