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Vietnam Contests
Vietnam National Olympiad
1994 Vietnam National Olympiad
1
solve system
solve system
Source: 32-th Vietnamese Mathematical Olympiad 1994
February 24, 2007
logarithms
algebra
system of equations
algebra proposed
Problem Statement
Find all real solutions to
x
3
+
3
x
−
3
+
ln
(
x
2
−
x
+
1
)
=
y
,
x^{3}+3x-3+\ln{(x^{2}-x+1)}=y,
x
3
+
3
x
−
3
+
ln
(
x
2
−
x
+
1
)
=
y
,
y
3
+
3
y
−
3
+
ln
(
y
2
−
y
+
1
)
=
z
,
y^{3}+3y-3+\ln{(y^{2}-y+1)}=z,
y
3
+
3
y
−
3
+
ln
(
y
2
−
y
+
1
)
=
z
,
z
3
+
3
z
−
3
+
ln
(
z
2
−
z
+
1
)
=
x
.
z^{3}+3z-3+\ln{(z^{2}-z+1)}=x.
z
3
+
3
z
−
3
+
ln
(
z
2
−
z
+
1
)
=
x
.
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