Pertanyaan

Jika k memenuhi persamaan x 2 + x − 1 4 x 2 + 3 x + 1 = 2 ,maka k + 4 = ...

Jika k memenuhi persamaan $\frac{4 x ^{2} + 3 x + 1}{x ^{2} + x - 1} = 2$ , maka $k + 4 =$ ...

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Jawaban terverifikasi

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Pembahasan

Perhatikan bahwa Cek hasil yang telah didapatkan ke dalam persamaan semula. Untuk x = 5 didapat ruas kiri yaitu Karena ruas kanannya sama dengan 2, maka ruas kiri = ruas kanan. Sehingga x = 5 memenuhi persamaan tersebut. Maka didapat k = 5 . Sehingga

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of fraction numerator 4 x squared plus 3 x plus 1 over denominator x squared plus x minus 1 end fraction end root end cell equals 2 row cell open parentheses square root of fraction numerator 4 x squared plus 3 x plus 1 over denominator x squared plus x minus 1 end fraction end root close parentheses squared end cell equals cell 2 squared end cell row cell fraction numerator 4 x squared plus 3 x plus 1 over denominator x squared plus x minus 1 end fraction end cell equals 4 row cell 4 x squared plus 3 x plus 1 end cell equals cell 4 open parentheses x squared plus x minus 1 close parentheses end cell row cell 4 x squared plus 3 x plus 1 end cell equals cell 4 x squared plus 4 x minus 4 end cell row cell 4 x squared plus 3 x plus 1 minus 4 x squared minus 4 x plus 4 end cell equals 0 row cell negative x plus 5 end cell equals 0 row cell negative x end cell equals cell negative 5 end cell row x equals 5 end table end style$

Cek hasil yang telah didapatkan ke dalam persamaan semula.

Untuk x = 5 didapat ruas kiri yaitu

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of fraction numerator 4 x squared plus 3 x plus 1 over denominator x squared plus x minus 1 end fraction end root end cell equals cell square root of fraction numerator 4 open parentheses 5 close parentheses squared plus 3 open parentheses 5 close parentheses plus 1 over denominator 5 squared plus 5 minus 1 end fraction end root end cell row blank equals cell square root of fraction numerator 4 open parentheses 25 close parentheses plus 15 plus 1 over denominator 25 plus 5 minus 1 end fraction end root end cell row blank equals cell square root of fraction numerator 100 plus 15 plus 1 over denominator 25 plus 5 minus 1 end fraction end root end cell row blank equals cell square root of 116 over 29 end root end cell row blank equals cell square root of 4 end cell row blank equals 2 end table end style$

Karena ruas kanannya sama dengan 2, maka ruas kiri = ruas kanan. Sehingga x = 5 memenuhi persamaan tersebut.

Maka didapat k = 5.

Sehingga