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2021 Romania National Olympiad
3
System of two equations
System of two equations
Source: Romania NMO 2021 grade 8
April 25, 2021
algebra
Problem Statement
Solve the system in reals:
(
x
+
x
2
+
1
)
(
y
+
y
2
+
1
)
=
2022
(x+\sqrt{x^2+1})(y+\sqrt{y^2+1})=2022
(
x
+
x
2
+
1
)
(
y
+
y
2
+
1
)
=
2022
and
x
+
y
=
2021
2022
x+y=\frac{2021}{\sqrt{2022}}
x
+
y
=
2022
2021
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