Răspuns:
x apartine {6;7}
Explicație pas cu pas:
x-1apartine {1;2...;7}
x apartine {1;2...7}
intersectand, ramane x apartine {2;3;...7}
observam ca
7-(x-1) =7-x+1=8-x
atunci
7!/((x-1)!*(8-x)!)≥ 2*7!/(x!*(7-x)!)
simplificam cu 7!/((x-1)!(7-x)!)
1/(8-x)≥2/x
x≥ 2(8-x)
3x≥16
x≥16/3 si x∈N
deci x∈{6;7;...}
dar x apartine {2;3;...7}
aplicand C.E , x∈{6;7}
verificare
pt x=6
Comb de 7 luate cate 5 ≥2 Comb de 7 luate cate 6
2*7!/2*5!≥ 14....42≥14 Adevarat
Pt x=7
Comb de 7 luate cate 6>2 Comb de 7 luate cate 7
7>2*1 A
