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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2022 Bosnia and Herzegovina Junior BMO TST
1
1
Part of
2022 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
JBMO TST- Bosnia and Herzegovina 2022 P1
Source: JBMO TST 2022 Bosnia and Herzegovina P1
5/21/2022
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be real numbers such that
a
2
−
b
c
=
b
2
−
c
a
=
c
2
−
a
b
=
2
a^2-bc=b^2-ca=c^2-ab=2
a
2
−
b
c
=
b
2
−
c
a
=
c
2
−
ab
=
2
. Find the value of
a
b
+
b
c
+
c
a
ab+bc+ca
ab
+
b
c
+
c
a
and find at least one triplet
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
that satisfy those conditions.
JBMO TST
algebra
national olympiad