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Ireland Contests
Ireland National Math Olympiad
2017 Irish Math Olympiad
2
a + b + c = 0 , a^2 + b^2 + c^2 = 1 , a^3 + b^3 +c^3 = 4abc
a + b + c = 0 , a^2 + b^2 + c^2 = 1 , a^3 + b^3 +c^3 = 4abc
Source: Irish MO 2017 paper 1 problem 2
December 12, 2022
algebra
system of equations
System
Problem Statement
Solve the equations :
{
a
+
b
+
c
=
0
a
2
+
b
2
+
c
2
=
1
a
3
+
b
3
+
c
3
=
4
a
b
c
\begin{cases} a + b + c = 0 \\ a^2 + b^2 + c^2 = 1\\a^3 + b^3 +c^3 = 4abc \end{cases}
⎩
⎨
⎧
a
+
b
+
c
=
0
a
2
+
b
2
+
c
2
=
1
a
3
+
b
3
+
c
3
=
4
ab
c
for
a
,
b
,
a,b,
a
,
b
,
and
c
.
c.
c
.
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