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$i f x + \frac{1}{x} = 2; f i n d t h e v a l u e o f x^{17} + \frac{1}{x^{19}} = ?$
(Equation)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$G i v e n t h a t, x + \frac{1}{x} = 2 = \frac{x^{2} + 1}{x} = 2 = x^{2} + 1 = 2 x = x^{2} - 2 x + 1 = 0 = x^{2} - 2 \times x \times 1 + 1^{2} = 0 = {(x - 1)}^{2} = 0 = x - 1 = \sqrt{0} = 0 ∴ x = 1 ∴ T h e v a l u e o f x^{17} + \frac{1}{x^{19}} = 1^{17} + \frac{1}{1^{19}} = 1 + \frac{1}{1} = 1 + 1 = 2 ∴ x^{17} + \frac{1}{x^{19}} = 2 (A n s w e r)$