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Poland - Second Round
1955 Poland - Second Round
1
1
Part of
1955 Poland - Second Round
Problems
(1)
x^4 + y^4 + z^4=? if x + y + z = 0 and x^2 + y^2 + z^2 = a
Source: Polish MO second round 1955 p1
8/29/2024
Calculate the sum
x
4
+
y
4
+
z
4
x^4 + y^4 + z^4
x
4
+
y
4
+
z
4
knowing that
x
+
y
+
z
=
0
x + y + z = 0
x
+
y
+
z
=
0
and
x
2
+
y
2
+
z
2
=
a
x^2 + y^2 + z^2 = a
x
2
+
y
2
+
z
2
=
a
, where
a
a
a
is a given positive number.
algebra