Question

1. Determinati multimile: A = {x 6 | 6x+20 < 2x+56 si 2|x } B = {(x, y) | XEN, Y E N, astfel incat 3x+2y=12



Dau coroana ​

Answer 1

A=Ф (multimea vida)

*De altfel, daca x era intreg, atunci membrul stang era par, iar cel drept era impar.*

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(x+1)∈[-1;1] => x∈[-2;0], dar x∈N => x=0.

B={0}.

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Cum x∈N=> x∈{0;1;2;3;4;5} => C={0;1;2;3;4;5}.

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3x+2y=12=>3x=12-2y<=> 3x=2(6-y). Dar 2 si 3 sunt prime intre ele => 3 | 6-y si 2 | x. Mai mult, 3 | 6-y implica 3 | y.

Deci exista a,b∈N astfel incat x=2a si y=3b.

3x+2y=12<=>6a+6b=12 <=> a+b=2 => (a,b)∈{(0;2);(1;1);(2;0) => (x;y)∈{(0;6);(2;3);(4;0)}.

D={(0;6);(2;3);(4;0)}.

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Deci ∈{21; 42; 63; 84}.

E={21; 42; 63; 84}.