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Poland - Second Round
2020 Poland - Second Round
1.
Algebra problem
Algebra problem
Source: Poland - Second Round 2020 P1
February 8, 2020
algebra
Poland
Problem Statement
Assume that for pairwise distinct real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
holds:
(
a
2
+
b
2
−
1
)
(
a
+
b
)
=
(
b
2
+
c
2
−
1
)
(
b
+
c
)
=
(
c
2
+
d
2
−
1
)
(
c
+
d
)
.
(a^2+b^2-1)(a+b)=(b^2+c^2-1)(b+c)=(c^2+d^2-1)(c+d).
(
a
2
+
b
2
−
1
)
(
a
+
b
)
=
(
b
2
+
c
2
−
1
)
(
b
+
c
)
=
(
c
2
+
d
2
−
1
)
(
c
+
d
)
.
Prove that
a
+
b
+
c
+
d
=
0.
a+b+c+d=0.
a
+
b
+
c
+
d
=
0.
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