Question

[ARMY Jungkook]

1. Cho (a-b) chia hết cho 6

Chứng tỏ rằng: a+5b; a-13b; a+17b chia hết cho 6

2. Tìm x,y thuộc Z, biết:

a) (x+3)(y+2)=1
b) (2x-5)(y-6)=17

c) (x-1)(x+y)=33

Answer 1

[Nguyễn Lê Phước Thịnh]

Câu 2: 

a: (x+3)(y+2)=1

\(\Leftrightarrow\left(x+3;y+2\right)\in\left\{\left(-1;-1\right);\left(1;1\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(-4;-3\right);\left(-2;-3\right)\right\}\)

b: (2x-5)(y-6)=17

\(\Leftrightarrow\left(2x-5;y-6\right)\in\left\{\left(1;17\right);\left(17;1\right);\left(-1;-17\right);\left(-17;-1\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(3;23\right);\left(11;7\right);\left(2;-11\right);\left(-6;5\right)\right\}\)

c: \(\left(x-1\right)\left(x+y\right)=33\)

\(\Leftrightarrow\left(x-1;x+y\right)\in\left\{\left(1;33\right);\left(33;1\right);\left(-1;-33\right);\left(-33;-1\right);\left(3;11\right);\left(11;3\right);\left(-11;-3\right);\left(-3;-11\right)\right\}\)

hay \(\Leftrightarrow\left(x;x+y\right)\in\left\{\left(2;33\right);\left(34;1\right);\left(0;-33\right);\left(-32;-1\right);\left(4;11\right);\left(12;3\right);\left(-10;-3\right);\left(-2;-11\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(2;31\right);\left(34;-33\right);\left(0;-33\right);\left(-32;31\right);\left(4;7\right);\left(12;-9\right);\left(-10;7\right);\left(-2;-9\right)\right\}\)