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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
11.3
y=x^4+a , x=\1/y^4+b (III Soros Olympiad 1996-97 R1 11.3)
y=x^4+a , x=\1/y^4+b (III Soros Olympiad 1996-97 R1 11.3)
Source:
May 29, 2024
algebra
system of equations
Problem Statement
Find the greatest
a
a
a
for which there is
b
b
b
such that the system
{
y
=
x
4
+
a
x
=
1
y
4
+
b
\begin{cases} y=x^4+a \\ x=\dfrac{1}{y^4}+b \end{cases}
⎩
⎨
⎧
y
=
x
4
+
a
x
=
y
4
1
+
b
has exactly two solutions.
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