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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
10.4
2x2 radical system (III Soros Olympiad 1996-97 R2 10.4)
2x2 radical system (III Soros Olympiad 1996-97 R2 10.4)
Source:
May 31, 2024
system of equations
Problem Statement
Solve the system of equations
{
y
2
+
x
4
x
+
y
y
2
+
x
=
y
2
4
4
x
y
2
+
x
x
+
x
−
y
−
1
=
(
y
+
1
)
(
x
−
x
−
y
−
1
)
\begin{cases} \sqrt{\dfrac{y^2+x}{4x}}+\dfrac{y}{\sqrt{y^2+x}}=\dfrac{y^2}{4}\sqrt{\dfrac{4x}{y^2+x}} \\ \sqrt{x}+ \sqrt{x-y-1}=(y+1)(\sqrt{x}- \sqrt{x-y-1}) \end{cases}
⎩
⎨
⎧
4
x
y
2
+
x
+
y
2
+
x
y
=
4
y
2
y
2
+
x
4
x
x
+
x
−
y
−
1
=
(
y
+
1
)
(
x
−
x
−
y
−
1
)
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