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1986 Greece Junior Math Olympiad
4
(x^n+1/x^n) /(x^n-1/x^n) - Greece Juniors 1986 p4
(x^n+1/x^n) /(x^n-1/x^n) - Greece Juniors 1986 p4
Source:
September 13, 2024
algebra
Problem Statement
i) If
b
=
a
2
+
1
a
2
a
2
−
1
a
2
b=\dfrac{a^2+ \dfrac{1}{a^2}}{a^2-\dfrac{1}{a^2}}
b
=
a
2
−
a
2
1
a
2
+
a
2
1
, express
c
=
a
4
+
1
a
4
a
4
−
1
a
4
c=\dfrac{a^4+\dfrac{1}{a^4}}{a^4-\dfrac{1}{a^4}}
c
=
a
4
−
a
4
1
a
4
+
a
4
1
, in terms of
b
b
b
.ii) If
k
=
x
n
+
1
x
n
x
n
−
1
x
n
k= \frac{x^{n}+\dfrac{1}{x^{n}}}{x^{n}-\dfrac{1}{x^{n}}}
k
=
x
n
−
x
n
1
x
n
+
x
n
1
, express
m
=
x
2
n
+
1
x
2
n
x
2
n
−
1
x
2
n
m= \frac{x^{2n}+\dfrac{1}{x^{2n}}}{x^{2n}-\dfrac{1}{x^{2n}}}
m
=
x
2
n
−
x
2
n
1
x
2
n
+
x
2
n
1
in terms of
k
k
k
.
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