MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1998 India National Olympiad
2
2
Part of
1998 India National Olympiad
Problems
(1)
Rationals/irrationals
Source: INMO 1998 Prolem 2
10/6/2005
Let
a
a
a
and
b
b
b
be two positive rational numbers such that
a
3
+
b
3
\sqrt[3] {a} + \sqrt[3]{b}
3
a
+
3
b
is also a rational number. Prove that
a
3
\sqrt[3]{a}
3
a
and
b
3
\sqrt[3] {b}
3
b
themselves are rational numbers.
quadratics
algebra
number theory solved
number theory