let-be-a-b-such-as-a-2-b-2-ab-find-out-Z-a-n-b-n-a-n-b-n-when-a-0-

Question Number 75796 by ~blr237~ last updated on 17/Dec/19

let be a, b such as a^{2} - b^{2} = ab

find out Z = \frac{a^{n} + b^{n}}{a^{n} - b^{n}} when a \neq 0

Answered by mr W last updated on 17/Dec/19

a^{2} - b^{2} = ab

\frac{a}{b} - \frac{b}{a} = 1

l e t \frac{a}{b} = t

t - \frac{1}{t} = 1

t^{2} - t - 1 = 0

t = \frac{1 \pm \sqrt{5}}{2}

Z = \frac{a^{n} + b^{n}}{a^{n} - b^{n}} = \frac{t^{n} + 1}{t^{n} - 1} = 1 + \frac{2}{t^{n} - 1}

= 1 + \frac{2}{{(\frac{1 \pm \sqrt{5}}{2})}^{n} - 1}

Commented by ~blr237~ last updated on 17/Dec/19

You can't use 'macro parameter character #' in math mode

or let divide by a cause {it}^{'} s not null

Commented by mr W last updated on 17/Dec/19

{t h a t}^{'} s o b v i o u s .

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