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Problem
Problem
If
α
\alpha
α
is the number of solutions of
∣
x
∣
=
log
(
x
−
[
x
]
)
|x| = \log(x - [x])
∣
x
∣
=
lo
g
(
x
−
[
x
])
, (where
[
⋅
]
[\cdot]
[
⋅
]
denotes greatest integer function) and
lim
x
→
α
x
e
a
x
−
b
sin
x
x
3
\lim_{x \to \alpha} \frac{x e^{ax} - b \sin x}{x^3}
lim
x
→
α
x
3
x
e
a
x
−
b
s
i
n
x
is finite, the value of
(
a
−
b
)
(a - b)
(
a
−
b
)
is
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