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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
11.1
2x2 system with arcsin and radical (VI Soros Olympiad 1990-00 R2 11.1)
2x2 system with arcsin and radical (VI Soros Olympiad 1990-00 R2 11.1)
Source:
May 28, 2024
algebra
system of equations
Radicals
trigonometry
Problem Statement
Solve the system of equations
{
x
2
+
a
r
c
s
i
n
y
=
y
2
+
a
r
c
s
i
n
x
x
2
+
y
2
−
3
x
=
2
y
x
2
−
2
x
−
y
+
1
\begin{cases} x^2+arc siny =y^2+arcsin x \\ x^2+y^2-3x=2y\sqrt{x^2-2x-y}+1 \end{cases}
{
x
2
+
a
rcs
in
y
=
y
2
+
a
rcs
in
x
x
2
+
y
2
−
3
x
=
2
y
x
2
−
2
x
−
y
+
1
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