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lx-1l+lyl=0 =>x-1=0 và y=0
lx+1l+ly-yl=2 =>lx+1l+0=2 =>lx+1l=2 =>x+1=2 hoặc x+1=-2 =>x=1 hoặc x=-3
kẻ bảng
a,
\(\Rightarrow\)x,y-1 \(\in\)Ư(5)={-1;-5;1;5}
ta có bảng giá trị
x | -1 | -5 | 1 | 5 |
y-1 | -5 | -1 | 5 | 1 |
y | -4 | 0 | 6 | 2 |
Vậy các cặp số nguyên (x,y) là (-1,-4);(-5,0);(1,6);(5,2)
(x+1)(y+2)(2y-5)= 1 . 11.13
+ x+1 = 1 => x =0 => y+2=11 =>y=9 và 2y - 5 =13 => y =9 (TM) vậy x=0;y=9
hoặc y+2 =13 => y =11 và 2y-5 =11=> y= 8 loại
+x+1 = 11=> x =10 => y+2 =1 loại
=> y+2 = 13 => y= 11 và 2y-5 =1 => y=3 loại
+ x+1 = 13 => x=12 => y+2 =1 loại
=> y+2 =11 => y=9 và 2y -5 =1 => y=3 loại
Vậy x = 0 ; y = 9
a.
xy + 3x - 2y - 6 = 5
=>x(y + 3) - 2(y + 3) = 5
=>(x - 2)(y + 3) = 5.
Vì x, y thuộc Z nên x - 2, y + 3 thuộc Z
=> x - 2, y + 3 thuộc ước nguyên của 5
Lập bảng :
x - 2 | -5 | -1 | 1 | 5 |
y + 3 | -1 | -5 | 5 | 1 |
x | -3 | 1 | 3 | 7 |
y | -4 | -8 | 2 | -2 |
Vậy ......
b. Làm tương tự câu a.
c. Ta có x + y = 3 và x - y = 15
Bài này là tổng hiệu của cấp 1, áp dụng cách làm đó thì ta được số lớn là x = (3 + 15) : 2 = 9
Số bé là y = 9 - 15 = -6
d. Ta có : |x| + |y| = 1
=>|x| = 1 - |y|
Vì |x|, |y| >= 0 và |x| = 1 - |y| nên 0 =< |x|, |y| =< 1
Vì x, y thuộc Z nên x = 0 thì y = 1 hoặc -1 và ngược lại y = 0 thì x = 1 hoặc -1
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\(\left(x-2y\right)\left(y-1\right)=5\)
\(\Rightarrow\hept{\begin{cases}x-2y=5\\y-1=1\end{cases}}\) \(\Rightarrow\hept{\begin{cases}x=9\\y=2\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x-2y=5\\y-1=-1\end{cases}}\) \(\Rightarrow\hept{\begin{cases}x=-5\\y=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x-2y=1\\y-1=5\end{cases}}\) \(\Rightarrow\hept{\begin{cases}x=13\\y=6\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x-2y=-1\\y-1=-5\end{cases}}\) \(\Rightarrow\hept{\begin{cases}x=9\\y=-4\end{cases}}\)