Matematică
CarolinaHelena
2015-11-12 21:47:45
Determinati perechile (x, y) de nr întregi nenule, pt care 2xy+6x-y=18
Răspunsuri la întrebare
ronironaldo
2015-11-13 01:16:41

[latex]2x(y+3)=18+y= extgreater x= frac{18+y}{2x(y+3)} [/latex] x,y ∈ Z=> 2y+6|(y+18) =>(2y+6)|(2y+36)=>(2y+6)|(2y+36-2y-6)=30 => D30(2y+6),D15(y+3) =>y+3∈(-15,-5,-3,-1,1,3,5,15) =>y∈(-18,-8,-6,-4,-2,0,2,12) =>x∈(0,-2,-1,-7,8,1,2,3) Perechile ( in caz ca nu iti dai seama).. sunt: (x;y):  (0;-18),(0;-8),(0;-6),(0;-4),(0;-2),(0;0),(0;2),(0;12) (-2;-18),(-2;-8),(-2;-6),(-2;-4),(-2;-2),(-2;0),(-2;2),(-2;12) (-1;-18),(-1;-8),(-1;-6),(-1;-4),(-1;-2),(-1;0),(-1;2),(-1;12) (-7;-18),(-7;-8),(-7;-6),(-7;-4),(-7;-2),(-7;0),(-7;2),(-7;12) (8;-18),(8;-8),(8;-6),(8;-4),(8;-2),(8;0),(8;2),(8;12) (1;-18),(1;-8),(1;-6),(1;-4),(1;-2),(1;0),(1;2),(1;12) (2;-18),(2;-8),(2;-6),(2;-4),(2;-2),(2;0),(2;2),(2;12) (3;-18),(3;-8),(3;-6),(3;-4),(3;-2),(3;0),(3;2),(3;12)

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