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Math Prize For Girls Problems
2023 Math Prize for Girls Problems
16
16
Part of
2023 Math Prize for Girls Problems
Problems
(1)
Math Prize 2023 Problem 16
Source:
10/11/2023
Let
f
(
x
)
=
x
2
ā
3
/
4
f(x) = x^2 - 3/4
f
(
x
)
=
x
2
ā
3/4
. Let
f
(
n
)
(
x
)
f^{(n)}(x)
f
(
n
)
(
x
)
denote the composition of
f
f
f
with itself
n
n
n
times. For example,
f
(
3
)
(
x
)
=
f
(
f
(
f
(
x
)
)
)
f^{(3)}(x) = f(f(f(x)))
f
(
3
)
(
x
)
=
f
(
f
(
f
(
x
)))
. Let
R
R
R
be the set of complex numbers that is the union of the roots of the polynomials
f
(
n
)
(
x
2
+
3
/
4
)
f^{(n)}(x^2 + 3/4)
f
(
n
)
(
x
2
+
3/4
)
over positive integers
n
n
n
. Let
B
B
B
be the smallest rectangle in the complex plane with sides parallel to the real and imaginary axes that contains
R
R
R
. What is the square of the area of
B
B
B
?