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Sweden Contests
Swedish Mathematical Competition
2011 Swedish Mathematical Competition
3
3
Part of
2011 Swedish Mathematical Competition
Problems
(1)
x - 1/y^2 = y - 1/z^2 = z - /x^2
Source: 2011 Swedish Mathematical Competition p3
4/30/2021
Find all positive real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
, such that
x
−
1
y
2
=
y
−
1
z
2
=
z
−
1
x
2
x - \frac{1}{y^2} = y - \frac{1}{z^2}= z - \frac{1}{x^2}
x
−
y
2
1
=
y
−
z
2
1
=
z
−
x
2
1
system of equations
System
algebra