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Pertanyaan

Jika a adalah penyelesaian persamaan begin mathsize 14px style 5 a plus open parentheses 2 a plus 3 close parentheses squared equals open parentheses 2 a plus 1 close parentheses open parentheses 2 a plus 3 close parentheses end style dan persamaan 2k(3+ 1) = 12, maka nilai k yang tepat adalah ….

  1. -5

  2. -6

  3. -7

  4. -8

A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai k yang tepat adalah -6.

Pembahasan

Dengan menggunakan perkalian suku dua pada kedua ruas maka diperoleh,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 a plus open parentheses 2 a plus 3 close parentheses squared end cell equals cell open parentheses 2 a plus 1 close parentheses open parentheses 2 a plus 3 close parentheses end cell row cell 5 a plus open parentheses 2 a close parentheses squared plus 2 open parentheses 2 a close parentheses open parentheses 3 close parentheses plus 3 squared end cell equals cell 2 a open parentheses 2 a close parentheses plus 1 open parentheses 2 a close parentheses plus 2 a open parentheses 3 close parentheses plus 1 open parentheses 3 close parentheses end cell row cell 5 a plus 4 a squared plus 12 a plus 9 end cell equals cell 4 a squared plus 2 a and 6 a plus 3 end cell row cell 4 a squared plus 17 a plus 9 end cell equals cell 4 a squared plus 8 a plus 3 end cell row cell 4 a squared plus 17 a plus 9 minus sign 4 a squared end cell equals cell 4 a squared plus 8 a plus 3 minus sign 4 a squared end cell row cell 17 a plus 9 end cell equals cell 8 a plus 3 end cell row cell 17 a plus 9 minus sign 8 a end cell equals cell 8 a plus 3 minus sign 8 a end cell row cell 9 a plus 9 end cell equals 3 row cell 9 a plus 9 minus sign 9 end cell equals cell 3 minus sign 9 end cell row cell 9 a end cell equals cell negative sign 6 end cell row cell fraction numerator 9 a over denominator 9 end fraction end cell equals cell fraction numerator negative sign 6 over denominator 9 end fraction end cell row a equals cell fraction numerator negative sign 6 division sign 3 over denominator 9 division sign 3 end fraction end cell row a equals cell negative sign 2 over 3 end cell end table end style  

Karena a juga merupakan penyelesaian dari persamaan 2k(3a + 1) = 12 maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 k open parentheses 3 a plus 1 close parentheses end cell equals 12 row cell 2 k open parentheses 3 open parentheses negative sign 2 over 3 close parentheses plus 1 close parentheses end cell equals 12 row cell 2 k open parentheses negative sign 2 plus 1 close parentheses end cell equals 12 row cell 2 k open parentheses negative sign 1 close parentheses end cell equals 12 row cell negative sign 2 k end cell equals 12 row cell fraction numerator negative sign 2 k over denominator negative sign 2 end fraction end cell equals cell fraction numerator 12 over denominator negative sign 2 end fraction end cell row k equals cell negative sign 6 end cell end table end style  

Jadi nilai k yang tepat adalah -6.

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