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

Question Number 89938 by jagoll last updated on 20/Apr/20

If x (x + 1) = 1

find {(x + 1)}^{3} - \frac{1}{{(x + 1)}^{3}}

Commented by john santu last updated on 20/Apr/20

l e t x + 1 = t \Rightarrow x = t - 1

\Rightarrow (t - 1) t = 1, t - 1 = \frac{1}{t}

t - \frac{1}{t} = 1 \Rightarrow {(t - \frac{1}{t})}^{3} = 1

t^{3} - 3 t + \frac{3}{t} - \frac{1}{t^{3}} = 1

t^{3} - \frac{1}{t^{3}} - 3 (t - \frac{1}{t}) = 1

t^{3} - \frac{1}{t^{3}} = 4 \Rightarrow {(x + 1)}^{3} - \frac{1}{{(x + 1)}^{3}} = 4