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Purple Comet Problems
2017 Purple Comet Problems
12
12
Part of
2017 Purple Comet Problems
Problems
(2)
Purple Comet 2017 MS Problem 12
Source:
4/14/2018
Let
x
x
x
,
y
y
y
, and
z
z
z
be real numbers such that
12
x
−
9
y
2
=
7
12x - 9y^2 = 7
12
x
−
9
y
2
=
7
6
y
−
9
z
2
=
−
2
6y - 9z^2 = -2
6
y
−
9
z
2
=
−
2
12
z
−
9
x
2
=
4
12z - 9x^2 = 4
12
z
−
9
x
2
=
4
Find
6
x
2
+
9
y
2
+
12
z
2
6x^2 + 9y^2 + 12z^2
6
x
2
+
9
y
2
+
12
z
2
.
Purple Comet
Purple Comet 2017 HS problem 12
Source:
3/19/2020
Let
P
P
P
be a polynomial satisfying
P
(
x
+
1
)
+
P
(
x
−
1
)
=
x
3
P(x + 1) + P(x - 1) = x^3
P
(
x
+
1
)
+
P
(
x
−
1
)
=
x
3
for all real numbers
x
x
x
. Find the value of
P
(
12
)
P(12)
P
(
12
)
.
polynomial
algebra