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Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2003 Bosnia and Herzegovina Junior BMO TST
1
1
Part of
2003 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
w =\frac{3b + 2c}{6a}+\frac{2c + 6a}{3b}+\frac{6a + 3b}{2c} if 1/a+2/b+3/c=0
Source: 2003 Bosnia & Herzegovina JBMO TST p1
5/27/2020
Non-zero real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy the condition
1
a
+
2
b
+
3
c
=
0
\frac{1}{a}+\frac{2}{b}+\frac{3}{c}= 0
a
1
+
b
2
+
c
3
=
0
.Determine the value of
w
=
3
b
+
2
c
6
a
+
2
c
+
6
a
3
b
+
6
a
+
3
b
2
c
w =\frac{3b + 2c}{6a}+\frac{2c + 6a}{3b}+\frac{6a + 3b}{2c}
w
=
6
a
3
b
+
2
c
+
3
b
2
c
+
6
a
+
2
c
6
a
+
3
b
.
algebra