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2022 Poland - Second Round
1
Polish MO 2022 P1
Polish MO 2022 P1
Source: Polish MO 2022 P1
February 12, 2022
algebra
system of equations
Problem Statement
Find all real quadruples
(
a
,
b
,
c
,
d
)
(a,b,c,d)
(
a
,
b
,
c
,
d
)
satisfying the system of equations
{
a
b
+
c
d
=
6
a
c
+
b
d
=
3
a
d
+
b
c
=
2
a
+
b
+
c
+
d
=
6.
\left\{ \begin{array}{ll} ab+cd = 6 \\ ac + bd = 3 \\ ad + bc = 2 \\ a + b + c + d = 6. \end{array} \right.
⎩
⎨
⎧
ab
+
c
d
=
6
a
c
+
b
d
=
3
a
d
+
b
c
=
2
a
+
b
+
c
+
d
=
6.
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