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2013 Math Prize For Girls Problems
16
16
Part of
2013 Math Prize For Girls Problems
Problems
(1)
Math Prize 2013 Problem 16
Source:
9/10/2013
If
−
3
≤
x
<
3
2
-3 \le x < \frac{3}{2}
−
3
≤
x
<
2
3
and
x
≠
1
x \ne 1
x
=
1
, define
C
(
x
)
=
x
3
1
−
x
C(x) = \frac{x^3}{1 - x}
C
(
x
)
=
1
−
x
x
3
. The real root of the cubic
2
x
3
+
3
x
−
7
2x^3 + 3x - 7
2
x
3
+
3
x
−
7
is of the form
p
C
−
1
(
q
)
p C^{-1}(q)
p
C
−
1
(
q
)
, where
p
p
p
and
q
q
q
are rational numbers. What is the ordered pair
(
p
,
q
)
(p, q)
(
p
,
q
)
?