Question

Am nevoie de putin ajutor! :)

Answer 1

(√5+∛11)^90=(5^1/2+11^1/3)^90
se aplica formula termenului general
T(k+1)=Cde n luate cate k { 5^([90-k)/2) · 11^(k/3)
pentru a avea termeni rationali exponentii trebuie sa fie numere intregi, deci
" 90-k"  trebuie sa se divida cu 2,
deci k∈{ 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,
46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90 },
iar "k" trebuie sa se divida cu 3
k∈{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,
75,78,81,84,87,90 }, 
intersectia este
 k∈{ 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90}, deci avem 15 termeni rationali.