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Greece Junior Math Olympiad
2018 Greece Junior Math Olympiad
1
1
Part of
2018 Greece Junior Math Olympiad
Problems
(1)
Both numbers are rational
Source: Greece JMO 2018, pr1
3/5/2018
a) Does there exist a real number
x
x
x
such that
x
+
3
x+\sqrt{3}
x
+
3
and
x
2
+
3
x^2+\sqrt{3}
x
2
+
3
are both rationals? b) Does there exist a real number
y
y
y
such that
y
+
3
y+\sqrt{3}
y
+
3
and
y
3
+
3
y^3+\sqrt{3}
y
3
+
3
are both rationals?
rational number
algebra