MathDB
Problems
Contests
International Contests
IMO Longlists
1985 IMO Longlists
19
IMO LongList 1985 CYP2 - System of Simultaneous Equations
IMO LongList 1985 CYP2 - System of Simultaneous Equations
Source:
September 10, 2010
algebra proposed
algebra
Problem Statement
Solve the system of simultaneous equations
x
−
1
y
−
2
w
+
3
z
=
1
,
\sqrt x - \frac 1y - 2w + 3z = 1,
x
−
y
1
−
2
w
+
3
z
=
1
,
x
+
1
y
2
−
4
w
2
−
9
z
2
=
3
,
x + \frac{1}{y^2} - 4w^2 - 9z^2 = 3,
x
+
y
2
1
−
4
w
2
−
9
z
2
=
3
,
x
x
−
1
y
3
−
8
w
3
+
27
z
3
=
−
5
,
x \sqrt x - \frac{1}{y^3} - 8w^3 + 27z^3 = -5,
x
x
−
y
3
1
−
8
w
3
+
27
z
3
=
−
5
,
x
2
+
1
y
4
−
16
w
4
−
81
z
4
=
15.
x^2 + \frac{1}{y^4} - 16w^4 - 81z^4 = 15.
x
2
+
y
4
1
−
16
w
4
−
81
z
4
=
15.
Back to Problems
View on AoPS