Selesaikan setiap pertidaksamaan berikut. b. x−1x+1​​>1

Pertanyaan

Selesaikan setiap pertidaksamaan berikut.

b. square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

penyelesaian pertidaksamaan square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1 adalah x greater than 1

Pembahasan

Syarat:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x plus 1 over denominator x minus 1 end fraction end cell greater or equal than 0 end table
table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank less or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell 1 space atau space x end cell greater or equal than cell 1 space.... space left parenthesis 1 right parenthesis end cell end table  

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell not equal to 0 row x not equal to cell 1 space.... space left parenthesis 2 right parenthesis end cell end table

Untuk menyelesaikan pertidaksamaan  square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1 kuadrat kedua ruas, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root close parentheses squared end cell greater than cell 1 squared end cell row cell fraction numerator x plus 1 over denominator x minus 1 end fraction end cell greater than 1 row cell fraction numerator x plus 1 over denominator x minus 1 end fraction minus 1 end cell greater than 0 row cell fraction numerator x plus 1 minus left parenthesis x minus 1 right parenthesis over denominator x minus 1 end fraction end cell greater than 0 row cell fraction numerator x plus 1 minus x plus 1 over denominator x minus 1 end fraction end cell greater than 0 row cell fraction numerator 2 over denominator x minus 1 end fraction end cell greater than 0 row x greater than cell 1 space.... space left parenthesis 3 right parenthesis end cell end table

Iriskan (1), (2) dan (3) sehingga penyelesaian menjadi x greater than 1.

Jadi, penyelesaian pertidaksamaan square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1 adalah x greater than 1

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