Question 180

If $$\frac{x^{24}+1}{x^{12}}=7$$ then the value of $$\frac{x^{72}+1}{x^{36}}$$ is

Solution

$$\frac{x^{24}+1}{x^{12}}$$ = 7

We need to find, $$\frac{x^{72}+1}{x^{36}}$$ = $$x^{36} + \frac{1}{x^{36}}$$

=> $$x^{12} + \frac{1}{x^{12}}$$ = 7

Cubing both sides, and using the formula $$(a+b)^{3}$$ = $$a^{3}+b^{3}$$+ 3ab(a+b) , we get :

=> $$x^{36} + \frac{1}{x^{36}} + 3*1*(x^{12}+\frac{1}{x^{12}})$$ = 343

=> $$x^{36} + \frac{1}{x^{36}}$$ + 21 = 343

=> $$x^{36} + \frac{1}{x^{36}}$$ = 343-21 = 322

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