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1998 Ukraine National Math Olympiad
Problem 1
solve floor equation in one variable
solve floor equation in one variable
Source: Ukraine 1998 Grade 11 P1
June 6, 2021
floor function
algebra
equations
equation
Problem Statement
Solve the equation
1
+
{
2
x
}
=
⌊
x
2
⌋
+
2
⌊
x
⌋
+
3
\sqrt{1+\{2x\}}=\lfloor x^2\rfloor+2\lfloor x\rfloor+3
1
+
{
2
x
}
=
⌊
x
2
⌋
+
2
⌊
x
⌋
+
3
(where
{
a
}
=
a
−
⌊
a
⌋
\{a\}=a-\lfloor a\rfloor
{
a
}
=
a
−
⌊
a
⌋
).
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