Join WhatsApp Icon CAT WhatsApp Group
Question 128

If $$x + x^{-1} = 2$$, then the value of $$x^3 + x^{-3}$$ is:

Given, $$x+\dfrac{1}{x} = 2$$

Cubing on both sides

$$(x+\dfrac{1}{x})^3 = 2^3$$

=> $$x^3+\dfrac{1}{x^3}+3\times x\times \dfrac{1}{x}(x+\dfrac{1}{x}) = 8$$

=> $$x^3+\dfrac{1}{x^3}+3(2) = 8$$

Therefore, $$x^3+\dfrac{1}{x^3} = 8-6 = 2$$

Create a FREE account and get:

  • Free SSC Study Material - 18000 Questions
  • 230+ SSC previous papers with solutions PDF
  • 100+ SSC Online Tests for Free