MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2010 Junior Balkan Team Selection Tests - Moldova
1
(1/a +1/b)(1/c +1/d)+1/ab +1/cd=6 /\sqrt{abcd}
(1/a +1/b)(1/c +1/d)+1/ab +1/cd=6 /\sqrt{abcd}
Source: 2010 Moldova JBMO TST p1
February 25, 2021
algebra
Problem Statement
The positive real numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
satisfy the equality
(
1
a
+
1
b
)
(
1
c
+
1
d
)
+
1
a
b
+
1
c
d
=
6
a
b
c
d
\left(\frac{1}{a}+ \frac{1}{b}\right) \left(\frac{1}{c}+ \frac{1}{d}\right) + \frac{1}{ab}+ \frac{1}{cd} = \frac{6}{\sqrt{abcd}}
(
a
1
+
b
1
)
(
c
1
+
d
1
)
+
ab
1
+
c
d
1
=
ab
c
d
6
Find the value of the
a
2
+
a
c
+
c
2
b
2
−
b
d
+
d
2
\frac{a^2+ac+c^2}{b^2-bd+d^2}
b
2
−
b
d
+
d
2
a
2
+
a
c
+
c
2
Back to Problems
View on AoPS