If x+(1/x)=3 find x^5 +(1/x^5 )


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Question Number 30092 by math1967 last updated on 16/Feb/18

$I f x + \frac{1}{x} = 3 f i n d x^{5} + \frac{1}{x^{5}}$
	Answered by math1967 last updated on 16/Feb/18

	$x + \frac{1}{x} = 3 ∴ x^{2} + \frac{1}{x^{2}} = 7 a n d x^{3} + \frac{1}{x^{3}} = 18$ $n o w (x^{2} + \frac{1}{x^{2}}) (x^{3} + \frac{1}{x^{3}}) = 7 \times 18$ $x^{5} + \frac{1}{x^{5}} + x + \frac{1}{x} = 126$ $x^{5} + \frac{1}{x^{5}} = 123$
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