Soal Jawab Olimpiade Matematika : Nilai Minimum

Posted by yusufsila | Thursday, 5 January 2017  at 08:45
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Diketahui bahwa  y = (x + 1)(x + 2)(x + 3)(x + 4) + 2013, tentukan nilai minimum dari y.

Jawaban :
LIHAT JAWABAN:
y   = (x + 1)(x + 4)(x + 2)(x + 3) + 2013
     = (x2 + 5x + 4)(x2 + 5x + 6) + 2013
     = (x2 + 5x)2 + 10(x2 + 5x) + 24 + 2013
     = (x2 + 5x)2 + 10(x2 + 5x) + 25 + 2012
     = (x2 + 5x + 5)2 + 2012  ≥  2012

Nilai minimum dari y adalah 2012.

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