a

c

+

c

a

=

a2+c2

ac

=

b2+2accosB

ac

=

b2

ac

+2cosB

∵S_△ABC=

1

2

BD•AC=

1

2

b²=

1

2

acsinB

∴

b2

ac

=sinB

∴

a

c

+

c

a

=sinB+2cosB=

5

sin（B+φ）≤

5

又

a

c

+

c

a

≥2

∴2≤

a

c

+

c

a

≤

5