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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
8.2
(x+y)/(x-y)+(x-y)/(x+y)=1999 (VI Soros Olympiad 1990-00 R1 8.2)
(x+y)/(x-y)+(x-y)/(x+y)=1999 (VI Soros Olympiad 1990-00 R1 8.2)
Source:
May 27, 2024
algebra
Problem Statement
Real numbers
x
x
x
and
y
y
y
it is know that
x
+
y
x
−
y
+
x
−
y
x
+
y
=
1999
\frac{x+y}{x-y}+\frac{x-y}{x+y}= 1999
x
−
y
x
+
y
+
x
+
y
x
−
y
=
1999
. Find the value of the expression
x
4
+
y
4
x
4
−
y
4
+
x
4
−
y
4
x
4
+
y
4
.
\frac{x^4+y^4}{x^4-y^4}+\frac{x^4-y^4}{x^4+y^4}.
x
4
−
y
4
x
4
+
y
4
+
x
4
+
y
4
x
4
−
y
4
.
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