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Switzerland Contests
Switzerland Team Selection Test
2002 Switzerland Team Selection Test
9
9
Part of
2002 Switzerland Team Selection Test
Problems
(1)
a^n +1a^n -2 >= n^2 (a +1/a -2 )
Source: Switzerland - Swiss TST 2002 p9
2/18/2020
For each real number
a
a
a
and integer
n
≥
1
n \ge 1
n
≥
1
prove the inequality
a
n
+
1
a
n
−
2
≥
n
2
(
a
+
1
a
−
2
)
a^n +\frac{1}{a^n} -2 \ge n^2 \left(a +\frac{1}{a} -2\right)
a
n
+
a
n
1
−
2
≥
n
2
(
a
+
a
1
−
2
)
and find the cases of equality.
inequalities
algebra