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Mathematics
Mathematics
Problem
Let the maximum and minimum values of
(
8
x
−
x
2
−
12
−
4
)
2
+
(
x
−
7
)
2
\left(\sqrt{8x - x^2 - 12} - 4\right)^2 + (x - 7)^2
(
8
x
−
x
2
−
12
−
4
)
2
+
(
x
−
7
)
2
,
x
∈
R
x \in \mathbb{R}
x
∈
R
be
M
M
M
and
m
m
m
, respectively. Then
M
2
−
m
2
M^2 - m^2
M
2
−
m
2
is equal to ________.
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