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2019 Irish Math Olympiad
7
7
Part of
2019 Irish Math Olympiad
Problems
(1)
ab + bc + ca =? if a + b + c = 0 and a^4 + b^4 + c^4 = 128
Source: 2019 Irish Mathematical Olympiad paper 2 p7
10/5/2020
Three non-zero real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
a
+
b
+
c
=
0
a + b + c = 0
a
+
b
+
c
=
0
and
a
4
+
b
4
+
c
4
=
128
a^4 + b^4 + c^4 = 128
a
4
+
b
4
+
c
4
=
128
. Determine all possible values of
a
b
+
b
c
+
c
a
ab + bc + ca
ab
+
b
c
+
c
a
.
algebra