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Mathematics
Problem
Suppose
f
(
x
)
=
e
a
x
+
e
b
x
f(x)=e^{ax}+e^{bx}
f
(
x
)
=
e
a
x
+
e
b
x
, where
a
≠
b
a\ne b
a
=
b
, and that
f
′
′
(
x
)
−
2
f
′
(
x
)
−
15
f
(
x
)
=
0
f''(x)-2f'(x)-15f(x)=0
f
′′
(
x
)
−
2
f
′
(
x
)
−
15
f
(
x
)
=
0
for all
x
x
x
. Then the value of
∣
a
b
∣
/
3
|ab|/3
∣
ab
∣/3
is .....
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