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District Olympiad
2014 District Olympiad
1
An equality and an inequality
An equality and an inequality
Source: Romanian District Olympiad 2014, Grade 6, P1
June 15, 2014
inequalities
algebra proposed
algebra
Problem Statement
Prove that: [*]
(
1
2
)
3
+
(
2
3
)
3
+
(
5
6
)
3
=
1
\displaystyle\left( \frac{1}{2}\right) ^{3}+\left( \frac{2}{3}\right)^{3}+\left( \frac{5}{6}\right) ^{3}=1
(
2
1
)
3
+
(
3
2
)
3
+
(
6
5
)
3
=
1
[*]
3
33
+
4
33
+
5
33
<
6
33
3^{33}+4^{33}+5^{33}<6^{33}
3
33
+
4
33
+
5
33
<
6
33
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