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$i f \frac{x^{24} + 1}{x^{12}} = 7$ then the value of $\frac{x^{72} + 1}{x^{36}}$ =?

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

$G i v e n t h a t, \frac{x^{24} + 1}{x^{12}} = 7 = \frac{x^{24}}{x^{12}} + \frac{1}{x^{12}} = 7 = x^{12} + \frac{1}{x^{12}} = 7 = {(x^{12} + \frac{1}{x^{12}})}^{3} = 7^{3} = x^{36} + \frac{1}{x^{36}} + \frac{3 \times x^{12} \times 1}{x^{12}} (x^{12} + \frac{1}{x^{12}}) = 343 = x^{36} + \frac{1}{x^{36}} + (3 \times 7) = 343 = x^{36} + \frac{1}{x^{36}} + 21 = 343 = x^{36} + \frac{1}{x^{36}} = 343 - 21 = 322 ∴ \frac{x^{72} + 1}{x^{36}} = 322 (a n s w e r)$