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2017 JBMO Shortlist
A2
A2
Part of
2017 JBMO Shortlist
Problems
(1)
minimum of \sqrt{\frac{a}{b(3a+2)}}+\sqrt{\frac{b}{a(3b+2)}}
Source: JBMO Shortlist 2017 A2
7/25/2018
Let
a
a
a
and
b
b
b
be positive real numbers such that
3
a
2
+
2
b
2
=
3
a
+
2
b
3a^2 + 2b^2 = 3a + 2b
3
a
2
+
2
b
2
=
3
a
+
2
b
. Find the minimum value of
A
=
a
b
(
3
a
+
2
)
+
b
a
(
2
b
+
3
)
A =\sqrt{\frac{a}{b(3a+2)}} + \sqrt{\frac{b}{a(2b+3)}}
A
=
b
(
3
a
+
2
)
a
+
a
(
2
b
+
3
)
b
algebra
minimum value
JBMO