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Mathematics
Problem
If the normals at the four points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
,
(
x
3
,
y
3
)
(x_1, y_1), (x_2, y_2), (x_3, y_3)
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
,
(
x
3
,
y
3
)
and
(
x
4
,
y
4
)
(x_4, y_4)
(
x
4
,
y
4
)
on the ellipse
x
2
a
2
+
y
2
b
2
=
1
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
a
2
x
2
+
b
2
y
2
=
1
are concurrent, then the value of
(
∑
i
=
1
4
x
i
)
(
∑
i
=
1
4
1
x
i
)
\left(\sum_{i=1}^{4} x_i\right) \left(\sum_{i=1}^{4} \frac{1}{x_i}\right)
(
∑
i
=
1
4
x
i
)
(
∑
i
=
1
4
x
i
1
)
is
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