MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1999 All-Russian Olympiad Regional Round
11.5
|x+a|+|x+y+b|+|y+c|>|x|+|x+y|+|y| - All-Russian MO 1999 Regional (R4) 11.5
|x+a|+|x+y+b|+|y+c|>|x|+|x+y|+|y| - All-Russian MO 1999 Regional (R4) 11.5
Source:
September 25, 2024
algebra
inequalities
Problem Statement
Are there real numbers
a
,
b
a, b
a
,
b
and
c
c
c
such that for all real
x
x
x
and
y
y
y
the following inequality holds:
∣
x
+
a
∣
+
∣
x
+
y
+
b
∣
+
∣
y
+
c
∣
>
∣
x
∣
+
∣
x
+
y
∣
+
∣
y
∣
?
|x + a| + |x + y + b| + |y + c| > |x| + |x + y| + |y|?
∣
x
+
a
∣
+
∣
x
+
y
+
b
∣
+
∣
y
+
c
∣
>
∣
x
∣
+
∣
x
+
y
∣
+
∣
y
∣
?
Back to Problems
View on AoPS