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Pertanyaan

Jika x subscript 1 dan x subscript 2 akar-akar persamaan 2 to the power of x plus 1 end exponent minus 1 over 2 to the power of x minus 3 end exponent equals 17, maka x subscript 1 squared plus x subscript 2 squared equals .... (UM UGM 2009) 

  1. 2 

  2. 5 

  3. 8 

  4. 10 

  5. 13 

W. Rohmiyati

Master Teacher

Mahasiswa/Alumni Universitas Langlangbuana

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D. 

Pembahasan

Pada soal diberikan 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of x plus 1 end exponent plus 1 over 2 to the power of x minus 3 end exponent end cell equals 17 row cell 2 to the power of x times 2 to the power of 1 plus 2 to the power of negative x plus 3 end exponent end cell equals 17 row cell 2 times 2 to the power of x plus 2 to the power of negative x end exponent times 2 cubed end cell equals 17 row cell 2 times 2 to the power of x plus 1 over 2 to the power of x times 8 end cell equals 17 row cell misal space 2 to the power of x end cell equals a row cell 2 a plus 8 times 1 over a end cell equals 17 row cell 2 a squared plus 8 end cell equals cell 17 a end cell row cell 2 a squared minus 17 a plus 8 end cell equals 0 row cell left parenthesis 2 a minus 1 right parenthesis left parenthesis a minus 8 right parenthesis end cell equals 0 row blank blank blank end table 

Maka pembuat nol nya adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a minus 1 end cell equals cell 0 space end cell row a equals cell 1 half end cell row cell 2 to the power of x end cell equals cell 2 to the power of negative 1 end exponent end cell row x equals cell negative 1 end cell end table    atau    table attributes columnalign right center left columnspacing 0px end attributes row cell a minus 8 end cell equals 0 row a equals 9 row cell 2 to the power of x end cell equals 8 row cell 2 to the power of x end cell equals cell 2 cubed end cell row x equals 3 row blank blank blank end table 

Maka x subscript 1 equals negative 1 space dan space x subscript 2 equals 3 sehingga nilai 

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared end cell equals cell open parentheses negative 1 close parentheses squared plus left parenthesis 3 right parenthesis squared space end cell row blank equals cell 1 plus 9 end cell row blank equals 10 end table 

Oleh karena itu, jawaban yang benar adalah D. 

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