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Solusi 
Solusi OSN Matematika 2014 Part 2 
f (x) = 
2 
2 + 4x 
maka: 
f 
 
2 
2014 
 
= 
2 
2 + 4 
2 
2014 
f 
 
2012 
2014 
 
= 
2 
2 + 4 
2012 
2014 
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 1 / 4
Solusi 
f 
 
2 
2014 
 
+ f 
 
2012 
2014 
 
= 
2 
2 + 4 
2 
2014 
+ 
2 
2 + 4 
2012 
2014 
= 
2 
 
2 + 4 
2012 
2014 
 
+ 2 
 
2 + 4 
2 
2014 
 
 
2 + 4 
2 
2014 
  
2 + 4 
2012 
2014 
 
= 
4 + 2 
 
4 
2012 
2014 
 
+ 4 + 2 
 
4 
2 
2014 
 
4 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
+ 
 
4 
2012 
2014 
  
4 
2 
2014 
 
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 2 / 4
Solusi 
f 
 
2 
2014 
 
+ f 
 
2012 
2014 
 
= 
8 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
4 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
+ 4( 2012 
2014+ 2 
2014 ) 
= 
8 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
4 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
+ 41 
= 
8 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
8 + 2 
 
4 
2012 
2014 
 
+ 2 
 
4 
2 
2014 
 
= 1 
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 3 / 4
Solusi 
f 
 
2 
2014 
 
+ f 
 
2012 
2014 
 
= 1 
Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 4 / 4

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Mathematics Olympiad 2

  • 1. Solusi Solusi OSN Matematika 2014 Part 2 f (x) = 2 2 + 4x maka: f 2 2014 = 2 2 + 4 2 2014 f 2012 2014 = 2 2 + 4 2012 2014 Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 1 / 4
  • 2. Solusi f 2 2014 + f 2012 2014 = 2 2 + 4 2 2014 + 2 2 + 4 2012 2014 = 2 2 + 4 2012 2014 + 2 2 + 4 2 2014 2 + 4 2 2014 2 + 4 2012 2014 = 4 + 2 4 2012 2014 + 4 + 2 4 2 2014 4 + 2 4 2012 2014 + 2 4 2 2014 + 4 2012 2014 4 2 2014 Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 2 / 4
  • 3. Solusi f 2 2014 + f 2012 2014 = 8 + 2 4 2012 2014 + 2 4 2 2014 4 + 2 4 2012 2014 + 2 4 2 2014 + 4( 2012 2014+ 2 2014 ) = 8 + 2 4 2012 2014 + 2 4 2 2014 4 + 2 4 2012 2014 + 2 4 2 2014 + 41 = 8 + 2 4 2012 2014 + 2 4 2 2014 8 + 2 4 2012 2014 + 2 4 2 2014 = 1 Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 3 / 4
  • 4. Solusi f 2 2014 + f 2012 2014 = 1 Edy Wihardjo Soal Solusi Olimpiade Matematika 6 Mei 2014 4 / 4