Mathematics Olympiad 4

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Edy Wihardjo

Mathematics Olympiad

Bildung

Solusi
Solusi OSN Matematika 2014 Part 4
f (x) =
2
2 + 4x
maka:
f
a
2014

=
2
2 + 4
a
2014
f

2014 a
2014

=
2
2 + 4
2014a
2014
f
a
2014

+ f

2014 a
2014

=
2
2 + 4
a
2014
+
2
2 + 4
2014a
2014
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 1 / 1

Solusi
f
a
2014

+ f

2014 a
2014

=
2
2 + 4
a
2014
+
2
2 + 4
2014a
2014
=
2

2 + 4
2014a
2014

+ 2

2 + 4
a
2014

2 + 4
a
2014

2 + 4
2014a
2014

=
4 + 2

4
2014a
2014

+ 4 + 2

4
a
2014

4 + 2

4
2014a
2014

+ 2

4
a
2014

+

4
2014a
2014

4
a
2014

Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 2 / 1

Solusi
f
a
2014

+ f

2014 a
2014

=
8 + 2

4
2014a
2014

+ 2

4
a
2014

4 + 2

4
2014a
2014

+ 2

4
a
2014

+ 4( 2014a
2014 + a
2014 )
=
8 + 2

4
2014a
2014

+ 2

4
a
2014

4 + 2

4
2014a
2014

+ 2

4
a
2014

+ 41
=
8 + 2

4
2014a
2014

+ 2

4
a
2014

8 + 2

4
2014a
2014

+ 2

4
a
2014

= 1
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 3 / 1

Solusi
f
a
2014

+ f

2014 a
2014

= 1
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 4 / 1

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Mathematics Olympiad 4

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

2. Solusi f a 2014 + f 2014 a 2014 = 2 2 + 4 a 2014 + 2 2 + 4 2014a 2014 = 2 2 + 4 2014a 2014 + 2 2 + 4 a 2014 2 + 4 a 2014 2 + 4 2014a 2014 = 4 + 2 4 2014a 2014 + 4 + 2 4 a 2014 4 + 2 4 2014a 2014 + 2 4 a 2014 + 4 2014a 2014 4 a 2014 Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 2 / 1

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

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

Mathematics Olympiad 4

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Mathematics Olympiad 4