Mathematics Olympiad 4
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The document is a solution to a mathematics problem from an Indonesian mathematics olympiad in 2014. It involves calculating the sum of two functions, f(x) = 2/(2 + 4x) from a to 2014-a and solving for a. The solution shows the steps of adding the two functions, combining like terms and simplifying to arrive at the equation 8 + 2(4(2014-a/2014) + 2(4a/2014)) = 1.
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