MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2000 All-Russian Olympiad Regional Round
11.5
sum 1/\sqrt{1+x^2} <=2/\sqrt{1+xy} - All-Russian MO 2000 Regional (R4) 11.5
sum 1/\sqrt{1+x^2} <=2/\sqrt{1+xy} - All-Russian MO 2000 Regional (R4) 11.5
Source:
September 26, 2024
algebra
inequalities
Problem Statement
For non-negative numbers
x
x
x
and
y
y
y
not exceeding
1
1
1
, prove that
1
1
+
x
2
+
1
1
+
y
2
≤
2
1
+
x
y
,
\frac{1}{\sqrt{1+x^2}}+\frac{1}{\sqrt{1+y^2}} \le \frac{2}{\sqrt{1 + xy}},
1
+
x
2
1
+
1
+
y
2
1
≤
1
+
x
y
2
,
Back to Problems
View on AoPS