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Mathematics Olympiad 5

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Edy Wihardjo
Edy Wihardjo

Mathematics Olympiad

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

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Mathematics Olympiad 5

  • 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