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Junior Balkan MO
1997 Junior Balkan MO
2
compute the expression
compute the expression
Source: JBMO 1997, Problem 2
October 30, 2005
Problem Statement
Let
x
2
+
y
2
x
2
−
y
2
+
x
2
−
y
2
x
2
+
y
2
=
k
\frac{x^2+y^2}{x^2-y^2} + \frac{x^2-y^2}{x^2+y^2} = k
x
2
−
y
2
x
2
+
y
2
+
x
2
+
y
2
x
2
−
y
2
=
k
. Compute the following expression in terms of
k
k
k
:
E
(
x
,
y
)
=
x
8
+
y
8
x
8
−
y
8
−
x
8
−
y
8
x
8
+
y
8
.
E(x,y) = \frac{x^8 + y^8}{x^8-y^8} - \frac{ x^8-y^8}{x^8+y^8}.
E
(
x
,
y
)
=
x
8
−
y
8
x
8
+
y
8
−
x
8
+
y
8
x
8
−
y
8
.
Ciprus
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