MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Math Prize For Girls Problems
2022 Math Prize for Girls Problems
5
Math Prize 2022 Problem 5
Math Prize 2022 Problem 5
Source:
October 12, 2022
Problem Statement
Given a real number
a
a
a
, the floor of
a
a
a
, written
⌊
a
⌋
\lfloor a \rfloor
⌊
a
⌋
, is the greatest integer less than or equal to
a
a
a
. For how many real numbers
x
x
x
such that
1
≤
x
≤
20
1 \le x \le 20
1
≤
x
≤
20
is
x
2
+
⌊
2
x
⌋
=
⌊
x
2
⌋
+
2
x
?
x^2 + \lfloor 2x \rfloor = \lfloor x^2 \rfloor + 2x \, ?
x
2
+
⌊
2
x
⌋
=
⌊
x
2
⌋
+
2
x
?
Back to Problems
View on AoPS