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Mathematics
Mathematics
Problem
If the area of the region
{
(
x
,
y
)
:
∣
4
−
x
2
∣
≤
y
≤
x
2
,
y
≤
4
,
x
≥
0
}
\{(x, y) : |4 - x^2| \le y \le x^2, y \le 4, x \ge 0\}
{(
x
,
y
)
:
∣4
−
x
2
∣
≤
y
≤
x
2
,
y
≤
4
,
x
≥
0
}
is
(
80
2
α
−
β
)
\left(\frac{80\sqrt{2}}{\alpha} - \beta\right)
(
α
80
2
−
β
)
,
α
,
β
∈
N
\alpha, \beta \in \mathbb{N}
α
,
β
∈
N
, then
α
+
β
\alpha + \beta
α
+
β
is equal to ____.
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