已知1/a+1/b+1/c+1/d+1/36+1/45=1,且a,b,c,d为连续整数,求a,b,c,d.

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/18 10:47:41
已知1/a+1/b+1/c+1/d+1/36+1/45=1,且a,b,c,d为连续整数,求a,b,c,d.
xJ@_%-ɻe-A_@E]ԍB`AEI| O:QJ]ue&sK}=L b >NLSC-ue|^ճ.RfmŲTmْm$nuDďXC9HnUT58&wC+rA,VZ`:=*V\

已知1/a+1/b+1/c+1/d+1/36+1/45=1,且a,b,c,d为连续整数,求a,b,c,d.
已知1/a+1/b+1/c+1/d+1/36+1/45=1,且a,b,c,d为连续整数,求a,b,c,d.

已知1/a+1/b+1/c+1/d+1/36+1/45=1,且a,b,c,d为连续整数,求a,b,c,d.
1/a+1/b+1/c+1/d=19/20
1/3+1/4+1/5+1/6=19/20
所以a=3 b=4 c=5 d=6

1/a+1/b+1/c+1/d+1/36+1/45=1
1/a+1/b+1/c+1/d=19/20
不妨设a1/a>1/b>1/c>1/d
1/a+1/b+1/c+1/d<4/a
4/a>19/20,a<80/19,a<=4
试算
a=4,则b=5,c=6,d=7
1/a+1/b+1/c+1/d≠19/20,不合题意
a=3,则b=4,c=5,d=6
1/a+1/b+1/c+1/d=19/20符合题意
a+b+c+d=3+4+5+6=18