Question

47. If x² + x + 1=0, then what is the value of (x³+1/x³)³? (1) 8 (2) -1 (3) O (4) 1 (Andhra Pradesh, Stage-1, 2014-15)




Explain it please ​

Answer 1

Step-by-step explanation:

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