MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
10.8
ax^2+bx+c<1=1/\sqrt{1-x^2} (V Soros Olympiad 1998-99 Round 3 10.8)
ax^2+bx+c<1=1/\sqrt{1-x^2} (V Soros Olympiad 1998-99 Round 3 10.8)
Source:
May 26, 2024
inequalities
algebra
Problem Statement
It is known that for all
x
x
x
such that
∣
x
∣
<
1
|x| < 1
∣
x
∣
<
1
, the following inequality holds
a
x
2
+
b
x
+
c
≤
1
1
−
x
2
ax^2+bx+c\le \frac{1}{\sqrt{1-x^2}}
a
x
2
+
b
x
+
c
≤
1
−
x
2
1
Find the greatest value of
a
+
2
c
a + 2c
a
+
2
c
.
Back to Problems
View on AoPS