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Jika  adalah akar-akar dari persamaan,    dimana , maka nilai

Pertanyaan

Jika x subscript 1 space dan space x subscript 2 adalah akar-akar dari persamaan, 

9 to the power of x minus 4 times 3 to the power of x plus 1 end exponent minus 2 times 3 to the power of x plus 2 a equals 0 

dimana x subscript 1 plus x subscript 2 equals 3 times log presuperscript 3 space 2 plus 2, maka nilai a equals.... 

  1. 36space 

  2. 27space 

  3. 24space 

  4. 18space 

  5. 12space 

Pembahasan Soal:

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell 9 to the power of x minus 4 times 3 to the power of x plus 1 end exponent minus 2 times 3 to the power of x plus 2 a end cell equals 0 row cell x subscript 1 plus x subscript 2 end cell equals cell 3 times log presuperscript 3 space 2 plus 2 end cell end table 

Perhatikan bahwa persamaan eksponen yang diberikan dapat dinyatakan dalam bentuk persamaan kuadrat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 9 to the power of x minus 4 times 3 to the power of x plus 1 end exponent minus 2 times 3 to the power of x plus 2 a end cell equals 0 row cell open parentheses 3 to the power of x close parentheses squared minus 4 times open parentheses 3 to the power of x close parentheses times 3 minus 2 times open parentheses 3 to the power of x close parentheses plus 2 a end cell equals 0 row cell open parentheses 3 to the power of x close parentheses squared minus 12 times open parentheses 3 to the power of x close parentheses minus 2 times open parentheses 3 to the power of x close parentheses plus 2 a end cell equals 0 row cell open parentheses 3 to the power of x close parentheses squared minus 14 times open parentheses 3 to the power of x close parentheses plus 2 a end cell equals 0 end table 

Misalkan: Error converting from MathML to accessible text. maka diperoleh:

y squared table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 14 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table

Andaikan akar-akar dari persamaan kuadrat di atas adalah m space dan space n, maka diperoleh hubungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell m n end cell equals cell fraction numerator 2 a over denominator 1 end fraction end cell row blank equals cell 2 a end cell row m equals cell 3 to the power of x subscript 1 end exponent rightwards double arrow x subscript 1 equals log presuperscript 3 space m end cell row n equals cell 3 to the power of x subscript 1 end exponent rightwards double arrow x subscript 1 equals log presuperscript 3 space n end cell end table 

Karena diketahui x subscript 1 plus x subscript 2 equals 3 times log presuperscript 3 space 2 plus 2 maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell 3 times log presuperscript 3 space 2 plus 2 end cell row cell x subscript 1 plus x subscript 2 end cell equals cell log presuperscript 3 space m plus log presuperscript 3 space n end cell row cell log presuperscript 3 space m plus log presuperscript 3 space n end cell equals cell 3 times log presuperscript 3 space 2 plus 2 end cell row cell log presuperscript 3 space m n end cell equals cell log presuperscript 3 space 2 cubed plus log presuperscript 3 space 3 squared end cell row blank equals cell log presuperscript 3 space 8 plus log presuperscript 3 space 9 end cell row blank equals cell log presuperscript 3 space open parentheses 8 times 9 close parentheses end cell row cell log presuperscript 3 space m n end cell equals cell log presuperscript 3 space 72 end cell row cell m n end cell equals 72 row cell 2 a end cell equals 72 row a equals cell 72 over 2 end cell row a equals 36 end table 

Jadi, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Mei 2021

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