MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1979 All Soviet Union Mathematical Olympiad
276
ASU 276 All Soviet Union MO 1979 system (x-y\sqrt{x^2-y^2})/(\sqrt{1-x^2+y^2})=b
ASU 276 All Soviet Union MO 1979 system (x-y\sqrt{x^2-y^2})/(\sqrt{1-x^2+y^2})=b
Source:
July 14, 2019
algebra
system of equations
Problem Statement
Find
x
x
x
and
y
y
y
(
a
a
a
and
b
b
b
parameters):
{
x
−
y
x
2
−
y
2
1
−
x
2
+
y
2
=
a
y
−
x
x
2
−
y
2
1
−
x
2
+
y
2
=
b
\begin{cases} \dfrac{x-y\sqrt{x^2-y^2}}{\sqrt{1-x^2+y^2}} = a\\ \\ \dfrac{y-x\sqrt{x^2-y^2}}{\sqrt{1-x^2+y^2}} = b\end{cases}
⎩
⎨
⎧
1
−
x
2
+
y
2
x
−
y
x
2
−
y
2
=
a
1
−
x
2
+
y
2
y
−
x
x
2
−
y
2
=
b
Back to Problems
View on AoPS