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Ecuador Mathematical Olympiad (OMEC)
2023 Ecuador NMO (OMEC)
1
1
Part of
2023 Ecuador NMO (OMEC)
Problems
(1)
absolute value, squares and roots in the same dish
Source: OMEC Ecuador National Olympiad Final Round 2023 N3 P1 day 1
11/5/2024
Find all reals
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
such that
{
a
2
+
b
2
+
c
2
=
1
∣
a
+
b
∣
=
2
\begin{cases}a^2+b^2+c^2=1\\ |a+b|=\sqrt{2}\end{cases}
{
a
2
+
b
2
+
c
2
=
1
∣
a
+
b
∣
=
2
absolute value
algebra