MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2004 All-Russian Olympiad Regional Round
9.6
9.6
Part of
2004 All-Russian Olympiad Regional Round
Problems
(1)
sum \sqrt{xy +1}> x+ y + z - All-Russian MO 2004 Regional (R4) 9.6
Source:
9/27/2024
Positive numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
are such that the absolute value of the difference of any two of them are less than
2
2
2
. Prove that
x
y
+
1
+
y
z
+
1
+
z
x
+
1
>
x
+
y
+
z
.
\sqrt{xy +1}+\sqrt{yz + 1}+\sqrt{zx+ 1} > x+ y + z.
x
y
+
1
+
yz
+
1
+
z
x
+
1
>
x
+
y
+
z
.
algebra
inequalities