方程满足整数解的个数,x1+x2+x3+x4=19,0<=x1<=5,0<=x2<=6,3<=x3<=7,3<=x4<=8
时间: 2024-06-15 20:04:01 浏览: 14
要求方程满足整数解,且满足以下条件:
x1 + x2 + x3 + x4 = 19
0 <= x1 <= 5
0 <= x2 <= 6
3 <= x3 <= 7
3 <= x4 <= 8
我们可以使用组合数学中的方法来解决这个问题。首先,我们可以将方程转化为一个等价的问题,即求解以下方程:
y1 + y2 + y3 + y4 = 19 - (x1 + x2 + x3 + x4)
其中,y1 = x1, y2 = x2, y3 = x3 - 3, y4 = x4 - 3。
现在,我们需要求解新的方程:
y1 + y2 + y3 + y4 = 19 - (x1 + x2 + x3 + x4)
0 <= y1 <= 5
0 <= y2 <= 6
0 <= y3 <= 4
0 <= y4 <= 5
根据组合数学中的方法,我们可以使用组合数来计算整数解的个数。假设有n个物体要放入k个盒子中,每个盒子至少放一个物体,那么共有C(n-1, k-1)种放法。
根据上述方法,我们可以计算出方程满足整数解的个数为:
C(19 - (x1 + x2 + x3 + x4) + 4, 4)
相关推荐
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![py](https://img-home.csdnimg.cn/images/20210720083646.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![xlsx](https://img-home.csdnimg.cn/images/20210720083732.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![xlsx](https://img-home.csdnimg.cn/images/20210720083732.png)