Question

Tìm x ∈ N, biết:

a, x ∈ B(5), x < 20

b, x ⋮ 24; x ⋮ 45; 200 < x < 500

c, 452 = px+32; 321 = qx+21 (p,q ∈ N*)

Answer 1

a, Ta có: x ∈ B(5) = {0;5;10;15;20;25;...}

Mà x < 20 => x ∈ {0;5;10;15}

b, Ta có: x ⋮ 24; x ⋮ 45 => x ∈ BC{24;45}

24 = 2 3 . 3 ; 45 = 3 2 . 5 => BCNN(24;45) =  2 3 . 3 2 . 5 = 360

=> BC(24;45) = B(360) = {0;360;720;...}

Mà 200 < x < 500 => x = 360

c, Ta có:

452 = px+32 => 420 ⋮ x

321 = qx+21 => 320 ⋮ x

=> x ∈ ƯC(420;320)

420 =  2 2 . 3 . 5 . 7

320 =  2 6 . 5

=> ƯCLN(420;320) = 20 =  2 2 . 5

=> ƯC(420;320) = Ư(20) = {1;2;4;5;10;20}

Vậy x ∈ {1;2;4;5;10;20}