Question

Sa se determine multimile:A={x\x£ Z,2x-11\17} va roog repede si explicati-mi cum se face!!

Answer 1

(2x-11)/17.
x apartine Z=> 2x-11 divizibil cu 17=>

2x-11 apartine M (17)=>
2x-11 apartine {...-51; -34; 0; 17, 34, 51, 68, 85...}=>

2x apartine {..-40; -23; -11; 28; 35; 62; 79; 96; ...}=>

x apartine {..-20; -23/2; -11/2; 14; 35/2; 31; 79/2; 48; ...}

-23/2, -11/2, 35/3, 79/2.. nu apartin multimii numerelor intregi Z. =>


A={....-20; 14; 31; 48..}

Answer 2

Enunț:

Să se determine mulțimea  A = {x∈ Z;  2x -11|17}

R:

2x -11|17 ⇒ 2x - 11 ∈ D₁₇ ⇒ 2x - 11 ∈ {±1,  ±17} ⇒

⇒ 2x -11 ∈ {-17,  -1,  1,  17}|+11 ⇒ 2x ∈ {-6,  10,  12,  28}|:2 ⇒

⇒ x ∈ {-3,  5,  6,  14}

Deci,     A = {-3,  5,  6,  14}.