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Problem
Problem
Let
α
(
a
)
\alpha(a)
α
(
a
)
and
β
(
a
)
\beta(a)
β
(
a
)
be the roots of the equation
(
(
1
+
a
)
3
−
1
)
x
2
+
(
(
1
+
a
)
3
−
1
)
x
+
(
(
1
+
a
)
3
−
1
)
=
0
(\sqrt[3]{(1+a)} - 1)x^2 + (\sqrt[3]{(1+a)} - 1)x + (\sqrt[3]{(1+a)} - 1) = 0
(
3
(
1
+
a
)
−
1
)
x
2
+
(
3
(
1
+
a
)
−
1
)
x
+
(
3
(
1
+
a
)
−
1
)
=
0
, where
a
>
−
1
a > -1
a
>
−
1
, then
lim
a
→
0
+
α
(
a
)
\lim_{a \to 0^+} \alpha(a)
lim
a
→
0
+
α
(
a
)
and
lim
a
→
0
+
β
(
a
)
\lim_{a \to 0^+} \beta(a)
lim
a
→
0
+
β
(
a
)
are a.
(
−
5
2
)
\left(-\frac{5}{2}\right)
(
−
2
5
)
and 1 b.
(
−
1
2
)
\left(-\frac{1}{2}\right)
(
−
2
1
)
and
(
−
1
)
(-1)
(
−
1
)
c.
(
−
7
2
)
\left(-\frac{7}{2}\right)
(
−
2
7
)
and 2 d.
(
−
9
2
)
\left(-\frac{9}{2}\right)
(
−
2
9
)
and 3
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