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2021 Honduras National Mathematical Olympiad
Problem 2
Honduran National MO (OHM) Intermediate Problem 2
Honduran National MO (OHM) Intermediate Problem 2
Source: 2021 OHM Intermediate P2
November 21, 2021
algebra
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be real numbers such that
a
2
+
b
2
=
1
,
c
2
+
d
2
=
1
a^2+b^2=1,c^2+d^2=1
a
2
+
b
2
=
1
,
c
2
+
d
2
=
1
and
a
c
+
b
d
=
0
ac+bd=0
a
c
+
b
d
=
0
. Determine all possible values of
a
b
+
c
d
ab+cd
ab
+
c
d
.
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