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marina52
Pe: 2012-10-23T13:53:16+03:00 In: In:

Divizibilitate-cl.a 6-a-Mlgebra Ed.Taida

Determinati elementele multimilor:
A={x apartine lui N/x divide 3x+14 si x divide7x+30}
B={x apartine lui N/x+1 divide x+6}
C={x apartine lui N/2x+1 divide 5x+8
D={x apartine lui N*/x+1 divide 2x+17

Am rezolvat prin incercari,dar cred ca nu e corect.

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  1. edy8
    maestru (V)

    marina52 wrote: Determinati elementele multimilor:
    A={x apartine lui N/x divide 3x+14 si x divide7x+30}
    B={x apartine lui N/x+1 divide x+6}
    C={x apartine lui N/2x+1 divide 5x+8
    D={x apartine lui N*/x+1 divide 2x+17

    Am rezolvat prin incercari,dar cred ca nu e corect.

    \it{ D = \{x\in N^*[tex] \Large |[/tex] x+1|2x+17\}

    \it{\Large\bl x+1| 2x+17 (1)\\\;\\x+1| x+1\Rightarrow x+1| 2(x+1)\Rightarrow x+1| 2x+2 (2)\\\;\\(1), (2)\Rightarrow x+1| 2x+17-2x-2\Rightarrow x+1| 15\Rightarrow x+1\in D_{15}\Rightarrow\\\;\\\Rightarrow x+1 \in \{1, 3, 5, 15\}|_{ -1} \Rightarrow x\in \{0, 2, 4, 14\}\\\;\\Dar, x\in N^*.\\\;\\Deci, x\in \{2, 4, 14\} \Longrightarrow D = \{2, 4, 14\}}

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