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mada13
Pe: 2012-02-23T13:59:40+02:00 In: In:

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Determinati nr natural a astfel incat:

26 supra 28 < 13 supra 3n+2 < 2

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2 raspunsuri

  1. bedrix
    expert (VI)

    26 supra 28 < 13 supra 3n+2 < 2 este echivalenta cu 1/2<(3n+2)/13<28/26 aducem la acelasi numitor rezulta 13/26<(6n+4)/26<28/26 rezulta 13<6n+4<28 sau 9<6n<24 rezulta 9/6<n<4 rezulta n apartine {2,3}

  2. ambri
    veteran (III)

    \rm{\frac{26}{28} < \frac{13}{3n+2}<2.\\\;\\Avem de analizat doua inegalitati:\\\;\\I) \frac{26}{28} < \frac{13}{3n+2}\Rightarrow 26\cdot(3n+2)< 13\cdot28\bl |_{:13}\Rightarrow 2\cdot(3n+2) < 28|_{:2}\Rightarrow 3n+2 < 14 \\\;\\\Rightarrow 3n < 14-2\Rightarrow 3n< 12|_{:3} \Rightarrow n < 4\Rightarrow n\in \{0, 1, 2, 3\} (1)\\\;\\II) \frac{13}{3n+2}<2\Rightarrow \frac{13}{3n+2} < \frac{2}{1} \Rightarrow 13\cdot1 < 2\cdot (3n+2)\Rightarrow 13<6n+4\Rightarrow 6n+4>13\\\;\\\Rightarrow 6n>13-4\Rightarrow 6n>9|_{:3}\Rightarrow2n>3|_{:2}\Rightarrow n>\frac{3}{2} \Rightarrow n>1\frac{1}{2} (2)\\\;\\(1), (2) \Longrightarrow n\in\{2, 3\} }

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