If $$\frac{x^{32}-1}{x^{16}}=5$$, then find the value of $$\frac{x^{96}-1}{x^{48}}$$
Given : $$\frac{x^{32}-1}{x^{16}}=5$$
=> $$x^{16}-\frac{1}{x^{16}}=5$$ ---------------(i)
Cubing both sides, we get :
=> $$(x^{16}-\frac{1}{x^{16}})^3=(5)^3$$
=> $$x^48-\frac{1}{x^{48}}-3(x^{16})(\frac{1}{x^{16}})(x^{16}+\frac{1}{x^{16}})=125$$
=> $$x^{48}-\frac{1}{x^{48}}-3(5)=125$$
=>Â $$\frac{x^{96}-1}{x^{48}}=125+15=140$$
=> Ans - (C)
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