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Soros Olympiad in Mathematics
II Soros Olympiad 1995 - 96 (Russia)
10.4
2x2 system x+(x-y)/(x^2+y^2)=2 (II Soros Olympiad 1997-98 R3 10.4)
2x2 system x+(x-y)/(x^2+y^2)=2 (II Soros Olympiad 1997-98 R3 10.4)
Source:
June 6, 2024
algebra
system of equations
Problem Statement
Solve system of equations
{
x
+
x
+
y
x
2
+
y
2
=
1
x
+
x
−
y
x
2
+
y
2
=
2
\begin{cases} x+\dfrac{x+y}{x^2+y^2}=1 \\ x+\dfrac{x-y}{x^2+y^2}=2 \end{cases}
⎩
⎨
⎧
x
+
x
2
+
y
2
x
+
y
=
1
x
+
x
2
+
y
2
x
−
y
=
2
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