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3
Solutions to three equations of three variables
Solutions to three equations of three variables
Source: INAMO 2002 - Problem 3
August 5, 2011
algebra unsolved
algebra
Problem Statement
Find all solutions (real and complex) for
x
,
y
,
z
x,y,z
x
,
y
,
z
, given that:
x
+
y
+
z
=
6
x
2
+
y
2
+
z
2
=
12
x
3
+
y
3
+
z
3
=
24
x+y+z = 6 \\ x^2+y^2+z^2 = 12 \\ x^3+y^3+z^3 = 24
x
+
y
+
z
=
6
x
2
+
y
2
+
z
2
=
12
x
3
+
y
3
+
z
3
=
24
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