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2018 MOAA
8
2018 MOAA Team P8
2018 MOAA Team P8
Source:
January 23, 2022
algebra
team
2018
Problem Statement
Suppose that k and x are positive integers such that
k
2
=
(
1
+
3
2
)
x
+
(
1
−
3
2
)
x
.
\frac{k}{2}=\left( \sqrt{1 +\frac{\sqrt3}{2}}\right)^x+\left( \sqrt{1 -\frac{\sqrt3}{2}}\right)^x.
2
k
=
1
+
2
3
x
+
1
−
2
3
x
.
Find the sum of all possible values of
k
k
k
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