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Nilai yang memenuhi persamaan adalah ....

Nilai begin mathsize 14px style n end style yang memenuhi persamaan begin mathsize 14px style fraction numerator n factorial over denominator open parentheses n minus 2 close parentheses factorial cross times 4 factorial end fraction equals 10 end style adalah ....

  1. begin mathsize 14px style 10 end style 

  2. begin mathsize 14px style 12 end style 

  3. begin mathsize 14px style 13 end style 

  4. begin mathsize 14px style 15 end style 

  5. begin mathsize 14px style 16 end style 

Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator n factorial over denominator left parenthesis n minus 2 right parenthesis factorial cross times 4 factorial end fraction end cell equals 10 row cell fraction numerator n open parentheses n minus 1 close parentheses up diagonal strike open parentheses n minus 2 close parentheses factorial end strike over denominator up diagonal strike left parenthesis n minus 2 right parenthesis factorial end strike cross times 4 factorial end fraction end cell equals 10 row cell fraction numerator n squared minus n over denominator 4 times 3 times 2 times 1 end fraction end cell equals 10 row cell fraction numerator n squared minus n over denominator 24 end fraction end cell equals 10 row cell n squared minus n end cell equals 240 row cell n squared minus n minus 240 end cell equals 0 row cell open parentheses n plus 15 close parentheses open parentheses n minus 16 close parentheses end cell equals 0 row n equals cell negative 15 space end cell row n equals 16 end table end style 

Karena nilai begin mathsize 14px style n end style positif maka yang memenuhi adalah begin mathsize 14px style n equals 16 end style

Jadi, jawaban yang tepat adalah E.

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