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anytza
Pe: 2012-01-22T12:26:16+02:00 In: In:

ALGEBRA

Fie multimile A={x apartine Z/|x-1|<5} si B={x apartine Z, 4\x+1apartine Z}
a)Determinati multimile A si B
b)Calculati A intersectat cu B, AUB,A\B,B\A.

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3 raspunsuri

  1. andu_flavius95
    maestru (V)

        \[ \begin{array}{l} A = \left\{ {x \in Z|\left| {x - 1} \right| < 5} \right\} \\ \left| {x - 1} \right| < 5 \Rightarrow - 5 < x - 1 < 5 \Rightarrow - 4 < x < 6 \Rightarrow x \in \left[ { - 4,6} \right] \cap Z = \{ - 4,...,6\} \\ B = \left\{ {x \in Z|\frac{4}{{x + 1}} \in Z} \right\} \\ = > x + 1 \in D_4 \\ \Rightarrow x + 1 \in \left\{ { - 4, - 2, - 1,1,2,4} \right\} \\ \end{array} \]

  2. dan
    expert (VI)

    anytza wrote: Fie multimile A={x apartine Z/|x-1|<5} si B={x apartine Z, 4\x+1apartine Z}
    a)Determinati multimile A si B
    b)Calculati A intersectat cu B, AUB,A\B,B\A.


    \rm{Pentru ambele multimi trebuie sa determini valorile lui x conform conditiilor date;\\ (A) se cauta numerele intregi pt. care |x-1|<5 \Leftrightarrow -5<x-1<5 si rezolvam \\ inecuatiile "x-1>-5" si "x-1<5" . . . etc.\\ (B) se cauta valorile intregi pt. x astfel ca 4 \vdots (x+1) \\ adica: x+1=D_4=\{\pm1 ; \pm2 ; \pm4 \} . . . etc.\\\bl s.a.m.d.

  4. andu_flavius95
    maestru (V)

    Domunle Dan, se pare ca am trimis rezolvari chiar in acelasi timp, 🙂 Ce chestie

    Se mai intampla si minuni ❗
    Va doresc o seara placuta /( dan )

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