MathDB
Problems
Contests
International Contests
Baltic Way
2000 Baltic Way
18
18
Part of
2000 Baltic Way
Problems
(1)
Determine all real x,y
Source: Baltic Way 2000
12/17/2010
Determine all positive real numbers
x
x
x
and
y
y
y
satisfying the equation
x
+
y
+
1
x
+
1
y
+
4
=
2
⋅
(
2
x
+
1
+
2
y
+
1
)
x+y+\frac{1}{x}+\frac{1}{y}+4=2\cdot (\sqrt{2x+1}+\sqrt{2y+1})
x
+
y
+
x
1
+
y
1
+
4
=
2
⋅
(
2
x
+
1
+
2
y
+
1
)
number theory proposed
number theory