Đáp án:

\(\begin{array}{l} 1a)\,\,\,U\left( {60} \right) \cap B\left( 4 \right) = \left\{ {4;12;20;60} \right\}\\ b)\\ xy = 12 \Rightarrow \left( {x;y} \right) \in \left\{ {\left( {1;12} \right);\left( {12;1} \right);\left( {2;6} \right);\left( {6;2} \right);\left( {3;4} \right);\left( {4;3} \right)} \right\}\\ \left( {x + 1} \right)\left( {y - 1} \right) = 12 \Rightarrow \left( {x;y} \right) \in \left\{ {\left( {0;13} \right);\left( {11;2} \right);\left( {1;7} \right);\left( {5;3} \right);\left( {2;5} \right);\left( {3;4} \right)} \right\}\\ Bai\,\,3:\\ So\,\,luong\,\,cac\,uoc\,\,cua\,\,150\,\,la\,\,12\\ So\,\,luong\,\,cac\,uoc\,\,cua\,\,250\,\,la\,\,8\\ So\,\,luong\,\,cac\,uoc\,\,cua\,\,350\,\,la\,\,12\\ So\,\,luong\,\,cac\,uoc\,\,cua\,\,450\,\,la\,\,18\\ So\,\,luong\,\,cac\,uoc\,\,cua\,\,550\,\,la\,\,\,12 \end{array}\)

Giải thích các bước giải: \(\begin{array}{l} 1a)\,\,\\ U\left( {60} \right) = \left\{ {1;2;3;4;5;6;10;12;15;20;30;60} \right\}\\ B\left( 4 \right) = \left\{ {0;4;8;12;16;20;24;28;32;36;40;44;48;52;56;60;...} \right\}\\ \Rightarrow U\left( {60} \right) \cap B\left( 4 \right) = \left\{ {4;12;20;60} \right\}\\ b)\\ xy = 12\\ \Rightarrow \left( {x;y} \right) \in \left\{ {\left( {1;12} \right);\left( {12;1} \right);\left( {2;6} \right);\left( {6;2} \right);\left( {3;4} \right);\left( {4;3} \right)} \right\}\\ \left( {x + 1} \right)\left( {y - 1} \right) = 12\\ TH1:\,\,x + 1 = 1;\,\,y - 1 = 12 \Rightarrow x = 0;\,\,y = 13\\ TH2:\,\,x + 1 = 12;\,\,y - 1 = 1 \Rightarrow x = 11;\,\,y = 2\\ TH3:\,\,x + 1 = 2;\,\,y - 1 = 6 \Rightarrow x = 1;\,\,y = 7\\ TH4:\,\,x + 1 = 6;\,\,y - 1 = 2 \Rightarrow x = 5;\,\,y = 3\\ TH5:\,\,x + 1 = 3;\,\,y - 1 = 4 \Rightarrow x = 2;\,\,y = 5\\ TH6:\,\,x + 1 = 4;\,\,y - 1 = 3 \Rightarrow x = 3;\,\,y = 4\\ \Rightarrow \left( {x;y} \right) \in \left\{ {\left( {0;13} \right);\left( {11;2} \right);\left( {1;7} \right);\left( {5;3} \right);\left( {2;5} \right);\left( {3;4} \right)} \right\}\\ Bai\,\,3:\\ 150 = {2.3.5^2} \Rightarrow So\,\,luong\,\,cac\,uoc\,\,cua\,\,150\,\,la\,\,\left( {1 + 1} \right)\left( {1 + 1} \right)\left( {2 + 1} \right) = 12\\ 250 = {2.5^3} \Rightarrow So\,\,luong\,\,cac\,uoc\,\,cua\,\,250\,\,la\,\,\left( {1 + 1} \right)\left( {3 + 1} \right) = 8\\ 350 = {2.5^2}.7 \Rightarrow So\,\,luong\,\,cac\,uoc\,\,cua\,\,350\,\,la\,\,\left( {1 + 1} \right)\left( {2 + 1} \right)\left( {1 + 1} \right) = 12\\ 450 = {2.3^2}{.5^2} \Rightarrow So\,\,luong\,\,cac\,uoc\,\,cua\,\,450\,\,la\,\,\left( {1 + 1} \right)\left( {2 + 1} \right)\left( {2 + 1} \right) = 18\\ 550 = {2.5^2}.11 \Rightarrow So\,\,luong\,\,cac\,uoc\,\,cua\,\,550\,\,la\,\,\left( {1 + 1} \right)\left( {1 + 2} \right)\left( {1 + 1} \right) = 12 \end{array}\)