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Soros Olympiad in Mathematics
II Soros Olympiad 1995 - 96 (Russia)
9.2
(1-3a)/(2a + 3) >0, (17 + 4a)/(7 + a) (II Soros Olympiad 1995-96 R3 9.2)
(1-3a)/(2a + 3) >0, (17 + 4a)/(7 + a) (II Soros Olympiad 1995-96 R3 9.2)
Source:
June 4, 2024
algebra
inequalities
Problem Statement
The number
a
a
a
is such that both fractions
(
1
−
3
a
)
/
(
2
a
+
3
)
a
n
d
(
17
+
4
a
)
/
(
7
+
a
)
(1-3a)/(2a + 3) \,\,\, and \,\,\, (17 + 4a)/(7 + a)
(
1
−
3
a
)
/
(
2
a
+
3
)
an
d
(
17
+
4
a
)
/
(
7
+
a
)
are positive. Which one is closer to
5
\sqrt5
5
?
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