求{X+Y+Z=50 {1500X+2100Y+2500Z=90000 方程组的正整数解
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求{X+Y+Z=50{1500X+2100Y+2500Z=90000方程组的正整数解求{X+Y+Z=50{1500X+2100Y+2500Z=90000方程组的正整数解求{X+Y+Z=50{1500X
求{X+Y+Z=50 {1500X+2100Y+2500Z=90000 方程组的正整数解
求{X+Y+Z=50 {1500X+2100Y+2500Z=90000 方程组的正整数解
求{X+Y+Z=50 {1500X+2100Y+2500Z=90000 方程组的正整数解
1500X+2100Y+2500Z=90000化简为15X+21Y+25Z=900
你会发现影响式子相等的是Y,只有Y是5的倍数,式子才能
成立,正整数解只要令Y=5,10,15,20,25,30,35,40,
即可求出八组正整数解.
经过检验排除,Y= 25,30,35,40.X.Y无正整数解
最终解集为X=35,Y=5,Z=10
X=31,Y=10,Z=9
X=29,Y=15,Z=6
X=27,Y=20,Z=3
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由x+y=50-z ①
15x+21y=900-25z ②
②-①×15:
6y=150-10z
y=25-5z/3
令z=3t,y=25-5t
x=50-3t-25+5t=25+2t。
其中t∈N。
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