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araluca
Pe: 2012-09-20T17:52:28+03:00 In: In:

algebra

Aflati A intersectat cu B si A reunit cu B, daca:
a)A={x apartine lu Z cu proprietatea ca 3x+18/2x+5 apartine lui Z} si B={x apartine lui Z cu proprietatea ca 5x+12/2x+3 apartine lui Z}

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2 raspunsuri

  1. GreatMath
    veteran (III)

    Voi determina multimea A :

    \begin{array}{l} \frac{{3x + 18}}{{2x + 5}} = \frac{{2x + 5 + x + 13}}{{2x + 5}} = \frac{{2x + 5}}{{2x + 5}} + \frac{{x + 13}}{{2x + 5}} = 1 + \frac{{x + 13}}{{2x + 5}} \in Z \Leftrightarrow \frac{{x + 13}}{{2x + 5}} \in Z\\ \frac{{x + 13}}{{2x + 5}} \in Z \to 2\left( {\frac{{x + 13}}{{2x + 5}}} \right) \in Z \Rightarrow \frac{{2x + 26}}{{2x + 5}} = 1 + \frac{{21}}{{2x + 5}} \in Z \Leftrightarrow \frac{{21}}{{2x + 5}} \in Z\\ \frac{{21}}{{2x + 5}} \in Z \Leftrightarrow 2x + 5 \in {D_{21}} = \left\{ { \pm 1, \pm 3, \pm 7, \pm 21} \right\} \Rightarrow \\ \left\{ \begin{array}{l} 2x + 5 = \pm 1 \Rightarrow x = \left\{ { - 2, - 3} \right\}\\ 2x + 5 = \pm 3 \Rightarrow x = \left\{ { - 1, - 4} \right\}\\ 2x + 5 = \pm 7 \Rightarrow x = \left\{ {1, - 6} \right\}\\ 2x + 5 = \pm 21 \Rightarrow x = \left\{ {8, - 13} \right\} \end{array} \right. \Rightarrow A = \left\{ { - 13, - 6, - 4, - 3, - 2, - 1,1,8} \right\} \end{array}
    Sper ca nu am gresit la ecuatii …..
    Multimea B se determina asemănător ….

    Off-topic: după cum vezi este ceva de munca …..

  2. araluca

    Va multumesc mult!Mi-ati fost de mare ajutor!

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