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2022 Math Prize for Girls Problems
9
9
Part of
2022 Math Prize for Girls Problems
Problems
(1)
Math Prize 2022 Problem 9
Source:
10/12/2022
Let
△
P
Q
O
\triangle PQO
△
PQO
be the unique right isosceles triangle inscribed in the parabola
y
=
12
x
2
y = 12x^2
y
=
12
x
2
with
P
P
P
in the first quadrant, right angle at
Q
Q
Q
in the second quadrant, and
O
O
O
at the vertex
(
0
,
0
)
(0, 0)
(
0
,
0
)
. Let
△
A
B
V
\triangle ABV
△
A
B
V
be the unique right isosceles triangle inscribed in the parabola
y
=
x
2
/
5
+
1
y = x^2/5 + 1
y
=
x
2
/5
+
1
with
A
A
A
in the first quadrant, right angle at
B
B
B
in the second quadrant, and
V
V
V
at the vertex
(
0
,
1
)
(0, 1)
(
0
,
1
)
. The
y
y
y
-coordinate of
A
A
A
can be uniquely written as
u
q
2
+
v
q
+
w
uq^2 + vq + w
u
q
2
+
v
q
+
w
, where
q
q
q
is the
x
x
x
-coordinate of
Q
Q
Q
and
u
u
u
,
v
v
v
, and
w
w
w
are integers. Determine
u
+
v
+
w
u + v + w
u
+
v
+
w
.