Question

已知三个正实数a,b,c,满足a<b+c≤2a,b<a+c≤2b,则b/a的取值范围是?

谢谢!!!

Answer 1

a<b+c≤2a,
1<b/a+c/a<=2

b<a+c≤2b
b/a<1+c/a<=2b/a

2式相减得:
1-2b/a<b/a-1<2-b/a
2/3<b/a<3/2

Answer 2

a<b+c≤2a,
1<b/a+c/a<=2
b<a+c≤2b
b/a<1+c/a<=2b/a
2式相减得:
1-2b/a<b/a-1<2-b/a
2/3<b/a<3/2