Question 4

If $$\frac{x^{32}-1}{x^{16}}=5$$, then find the value of $$\frac{x^{96}-1}{x^{48}}$$

Solution

Given : $$\frac{x^{32}-1}{x^{16}}=5$$

=> $$x^{16}-\frac{1}{x^{16}}=5$$ ---------------(i)

Cubing both sides, we get :

=> $$(x^{16}-\frac{1}{x^{16}})^3=(5)^3$$

=> $$x^48-\frac{1}{x^{48}}-3(x^{16})(\frac{1}{x^{16}})(x^{16}+\frac{1}{x^{16}})=125$$

=> $$x^{48}-\frac{1}{x^{48}}-3(5)=125$$

=> $$\frac{x^{96}-1}{x^{48}}=125+15=140$$

=> Ans - (C)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: