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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2021 Bosnia and Herzegovina Junior BMO TST
1
1
Part of
2021 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
ab + c + d = 3, bc + d + a = 5, cd + a + b = 2, da + b + c = 6
Source: 2021 JBMO TST Bosnia and Herzegovina P1
10/7/2022
Determine all real numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
for which
a
b
+
c
+
d
=
3
ab + c + d = 3
ab
+
c
+
d
=
3
b
c
+
d
+
a
=
5
bc + d + a = 5
b
c
+
d
+
a
=
5
c
d
+
a
+
b
=
2
cd + a + b = 2
c
d
+
a
+
b
=
2
d
a
+
b
+
c
=
6
da + b + c = 6
d
a
+
b
+
c
=
6
algebra
system of equations