Question

Determinati x ∈ Z pentru care fractia -7x/2x+2 ∈ Z


25 Puncte

Answer 1

-7x/(2x+2)∈Z=>2x+2|-7x

2x+2|2x+2  

2x+2|-14x

2x+2|14x+14

________"+"

2x+2|14=>2x+2∈D₁₄=>2x+2∈{1;2;7;14} |-2=>2x∈{-1;0;5;12} |:2=>x∈{-1/2;0;5/2;6}

Answer 2

2x+2  I -7x    (2x+2 divide (-7x))

2x+2 I 2x+2    I × (-7)

2x+2 I (-7x)    I × 2

2x+2  I -14x-14

2x+2  I -14x

Scadem cele doua relatii

2x+2  I (-14)   ⇒   2x+2 ∈ D₋₁₄   ⇒   2x+2 ∈ {-14; -7; -2; -1; 1; 2; 7; 14}

2x+2 ∈ {-14; -7; -2; -1; 1; 2; 7; 14} I₋₂

2x ∈ {-16; -9; -4; -3; -1; 0; 5; 12} I÷₂

x ∈ {-8; -9/2; -2; -3/2; -1/2; 0; 5/2; 6}