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1971 Swedish Mathematical Competition
1
(1 + a + a^2 )^2 < 3 (1 + a^2 + a^4 )
(1 + a + a^2 )^2 < 3 (1 + a^2 + a^4 )
Source: 1971 Swedish Mathematical Competition p1
March 26, 2021
algebra
inequalities
Problem Statement
Show that
(
1
+
a
+
a
2
)
2
<
3
(
1
+
a
2
+
a
4
)
\left(1 + a + a^2\right)^2 < 3\left(1 + a^2 + a^4\right)
(
1
+
a
+
a
2
)
2
<
3
(
1
+
a
2
+
a
4
)
for real
a
≠
1
a \neq 1
a
=
1
.
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