Question 114

If $$x+\frac{1}{x}=5$$, then $$x^{6}+\frac{1}{x^{6}}$$ is

Solution

Expression : $$x+\frac{1}{x}=5$$

Cubing both sides, we get :

=> $$(x + \frac{1}{x})^3 = 5^3$$

=> $$x^3 + \frac{1}{x^3} + 3.x.\frac{1}{x}.(x + \frac{1}{x}) = 125$$

=> $$x^3 + \frac{1}{x^3} + 15 = 125$$

=> $$x^3 + \frac{1}{x^3} = 110$$

Now, squaring both sides, we get :

=> $$x^6 + \frac{1}{x^6} + 2 = 12100$$

=> $$x^6 + \frac{1}{x^6} = 12098$$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: