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Mathematics
Mathematics
Problem
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the length of three sides of a triangle satisfying the condition
(
a
2
+
b
2
)
x
2
−
2
b
(
a
+
c
)
⋅
x
+
(
b
2
+
c
2
)
=
0
(a^2 + b^2)x^2 - 2b(a + c) \cdot x + (b^2 + c^2) = 0
(
a
2
+
b
2
)
x
2
−
2
b
(
a
+
c
)
⋅
x
+
(
b
2
+
c
2
)
=
0
. If the set of all possible values of
x
x
x
is the interval
(
α
,
β
)
(\alpha, \beta)
(
α
,
β
)
, then
12
(
α
2
+
β
2
)
12(\alpha^2 + \beta^2)
12
(
α
2
+
β
2
)
is equal to:
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