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28 May, 20:19

Determinati numerele a si b stiind ca : (a, b) = 7 si a+b=28

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  1. 28 May, 22:12
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    Daca (a, b) = 7 = > 7 | a si 7 | b = > a=7x si b=7y, cu x, y ∈N * si (x, y) = 1.

    a+b=35 = > 7x+7y=35

    7 (x+y) = 35

    x+y=5

    x=1=>y=4 = > a=7 si b=28

    x=2=>y=3 = > a=14 si b=21

    x=3=>y=2 = > a=21 si b=14

    x=4=>y=1 = > a=28 si b=7

    Solutie: (a, b) ∈{ (7,28}; (14,21); (21,14); (28,7) }
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