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All-Russian Olympiad Regional Round
2003 All-Russian Olympiad Regional Round
10.5
10.5
Part of
2003 All-Russian Olympiad Regional Round
Problems
(1)
x^2 + y^2 + z^2 + 2xyz = 1 - All-Russian MO 2003 Regional (R4) 10.5
Source:
9/17/2024
Find all
x
x
x
for which the equation
x
2
+
y
2
+
z
2
+
2
x
y
z
=
1
x^2 + y^2 + z^2 + 2xyz = 1
x
2
+
y
2
+
z
2
+
2
x
yz
=
1
(relative to
z
z
z
) has a valid solution for any
y
y
y
.
algebra