Penyelesaian dari persamaan x+1−x−1x+1−x−1=31 adalah...

Pertanyaan

Penyelesaian dari persamaan $fraction numerator square root of x plus 1 end root minus square root of x minus 1 end root over denominator square root of x plus 1 end root minus square root of x minus 1 end root end fraction equals 1 third$ adalah...

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B

Pembahasan

Ingat kembali!

Untuk menentukan persamaan bentuk pangkat (irasional) maka kita dapat menyelesaiakannya dengan cara mengalikan dengan akar sekawan, kemudain jangan lupa untuk syarat persamaan bentuk akar:

square root of f open parentheses x close parentheses end root equals 0 rightwards arrow f open parentheses x close parentheses greater than 0

Sehingga diperoleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of x plus 1 end root plus square root of x minus 1 end root over denominator square root of x plus 1 end root minus square root of x minus 1 end root end fraction end cell equals cell 1 third end cell row cell fraction numerator square root of x plus 1 end root minus square root of x minus 1 end root over denominator square root of x plus 1 end root plus square root of x minus 1 end root end fraction cross times fraction numerator square root of x plus 1 end root minus square root of x minus 1 end root over denominator square root of x plus 1 end root minus square root of x minus 1 end root end fraction end cell equals cell 1 third end cell row cell fraction numerator open parentheses x plus 1 close parentheses minus 2 open parentheses square root of x plus 1 end root close parentheses open parentheses square root of x minus 1 end root close parentheses plus open parentheses x minus 1 close parentheses over denominator open parentheses x plus 1 close parentheses minus open parentheses x minus 1 close parentheses end fraction end cell equals cell 1 third end cell row cell fraction numerator negative 2 square root of x squared minus 1 end root plus 2 x over denominator 2 end fraction end cell equals cell 1 third end cell row cell negative square root of x squared minus 1 end root plus x end cell equals cell 1 third end cell row cell negative square root of x squared minus 1 end root end cell equals cell 1 third minus x end cell row cell square root of x squared minus 1 end root end cell equals cell negative 1 third plus x end cell row cell up diagonal strike x squared end strike minus 1 end cell equals cell 1 over 9 minus fraction numerator 2 x over denominator 3 end fraction plus up diagonal strike x squared end strike end cell row cell negative 9 end cell equals cell 1 minus 6 x end cell row cell negative 10 end cell equals cell negative 6 x end cell row x equals cell 10 over 6 end cell row x equals cell 5 over 3 end cell row blank blank blank end table$

Dengan demikian, penyelesaia dari persamaan tersebut adalah x equals 5 over 3

Jadi, jawaban yang tepat adalah B