mathematics olympiad
TRANSCRIPT
Soal Solusi Olimpiade Matematika
Edy Wihardjo
5 Mei 2014
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 1 / 7
Soal
Soal OSN Matematika 2014 Tingkat Propinsi
Diketahui
f (x) =2
2 + 4x
tentukan
f
(1
2014
)+ f
(2013
2014
)
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 2 / 7
Solusi
Solusi OSN Matematika 2014
f (x) =2
2 + 4x
f
(1
2014
)=
2
2 + 41
2014
f
(2013
2014
)=
2
2 + 420132014
f
(1
2014
)+ f
(2013
2014
)=
2
2 + 41
2014
+2
2 + 420132014
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 3 / 7
Solusi
=2
2 + 41
2014
+2
2 + 420132014
=2×
(2 + 4
20132014
)+ 2×
(2 + 4
12014
)(2 + 4
12014
)(2 + 4
20132014
)
=4 + 2
(4
20132014
)+ 4 + 2
(4
12014
)4 + 2
(4
20132014
)+ 2
(4
12014
)+(4
20132014
)(4
12014
)
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 4 / 7
Solusi
=4 + 2
(4
20132014
)+ 4 + 2
(4
12014
)4 + 2
(4
20132014
)+ 2
(4
12014
)+(4
20132014
)(4
12014
)
=8 + 2
(4
20132014
)+ 2
(4
12014
)4 + 2
(4
20132014
)+ 2
(4
12014
)+ 4
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 5 / 7
Solusi
=8 + 2
(4
20132014
)+ 2
(4
12014
)8 + 2
(4
20132014
)+ 2
(4
12014
)= 1
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 6 / 7
Solusi
Jika diketahui:
f (x) =2
2 + 4x
maka
f
(1
2014
)+ f
(2013
2014
)= 1
Edy Wihardjo Soal Solusi Olimpiade Matematika 5 Mei 2014 7 / 7