Mathematics Olympiad

1. Solusi
Solusi OSN Matematika 2014 Part 5
f (x) =
2
2 + 4x
maka:
f
a
a + b
=
2
2 + 4
a
a+b
f
b
a + b
=
2
2 + 4
b
a+b
f
a
a + b
+ f
b
a + b
=
2
2 + 4
a
a+b
+
2
2 + 4
b
a+b
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 1 / 4

2. Solusi
f
a
a + b
+ f
b
a + b
=
2
2 + 4
a
a+b
+
2
2 + 4
b
a+b
=
2
2 + 4
b
a+b
+ 2
2 + 4
a
a+b
2 + 4
a
a+b
2 + 4
b
a+b
=
4 + 2
4
b
a+b
+ 4 + 2
4
a
a+b
4 + 2
4
b
a+b
+ 2
4
a
a+b
+
4
b
a+b
4
a
a+b
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 2 / 4

3. Solusi
f
a
a + b
+ f
b
a + b
=
8 + 2
4
b
a+b
+ 2
4
a
a+b
4 + 2
4
b
a+b
+ 2
4
a
a+b
+ 4( b
a+b+ a
a+b )
=
8 + 2
4
b
a+b
+ 2
4
a
a+b
4 + 2
4
b
a+b
+ 2
4
a
a+b
+ 41
=
8 + 2
4
b
a+b
+ 2
4
a
a+b
8 + 2
4
b
a+b
+ 2
4
a
a+b
= 1
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 3 / 4

4. Solusi
f
a
a + b
+ f
b
a + b
= 1
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 4 / 4