If-x-1-x-3-find-x-5-1-x-5-

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

Facebook Tweet Pin