MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
1960 Poland - Second Round
1
1
Part of
1960 Poland - Second Round
Problems
(1)
a^{2n} + a^{2n-1}b + a^{2n-2} b^2 + \ldots + ab^{2n-1} + b^{2n} > 0
Source: Polish MO Second Round 1960 p1
8/31/2024
Prove that if the real numbers
a
a
a
and
b
b
b
are not both equal to zero, then for every natural
n
n
n
a
2
n
+
a
2
n
−
1
b
+
a
2
n
−
2
b
2
+
…
+
a
b
2
n
−
1
+
b
2
n
>
0.
a^{2n} + a^{2n-1}b + a^{2n-2} b^2 + \ldots + ab^{2n-1} + b^{2n} > 0.
a
2
n
+
a
2
n
−
1
b
+
a
2
n
−
2
b
2
+
…
+
a
b
2
n
−
1
+
b
2
n
>
0.
Sum
algebra
inequalities