If-x-5-3-then-x-3-1-x-3-or-is-it-possible-at-all-

Question Number 122174 by AbdullahMohammadNurusSafa last updated on 14/Nov/20

I f x = \sqrt{5} + \sqrt{3}, t h e n x^{3} + \frac{1}{x^{3}} = ?

o r, i s i t p o s s i b l e a t a l l ?

Answered by behi83417@gmail.com last updated on 14/Nov/20

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

= (5 \sqrt{5} + 3 \sqrt{3} + 15 \sqrt{3} + 27 \sqrt{5}) - 3 (\sqrt{5} + \sqrt{3}) =

= 29 \sqrt{5} + 15 \sqrt{3} .