Pertidaksamaan irasional x2−x​<2​ mempunyai himpunan penyelesaian ...

Pertanyaan

Pertidaksamaan irasional square root of x squared minus x end root less than square root of 2 mempunyai himpunan penyelesaian ...

  1. left curly bracket x vertical line minus 1 less than x less than 2 right curly bracket 

  2. left curly bracket x vertical line minus 1 less than x less or equal than 2 right curly bracket 

  3. left curly bracket x vertical line minus 1 less or equal than x less or equal than 2 right curly bracket 

  4. left curly bracket x vertical line minus 1 less than x less or equal than 0 space atau space 1 less or equal than x less than 2 right curly bracket 

  5. left curly bracket x vertical line minus 1 less or equal than x less or equal than 0 space atau space 1 less or equal than x less or equal than 2 right curly bracket 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Cara menyelesaikan Ptl:

  1. Tinjau syarat numerus, yaitu f left parenthesis x right parenthesis greater or equal than 0 space dan space g left parenthesis x right parenthesis greater or equal than 0
  2. Kuadratkan kedua ruas dan selesaikan sesuai bentuk pertidaksamaan yang terjadi.
  3. Penyelesaiannya merupakan irisan 1 dan 2.

Syarat numerus:

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus x end cell greater or equal than 0 row cell x open parentheses x minus 1 close parentheses end cell greater or equal than 0 end table 
x equals 0 space atau space x equals 1 

x less or equal than 0 space atau thin space x greater or equal than 1  

Proses menghilangkan akar:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of x squared minus x end root end cell less than cell square root of 2 end cell row cell open parentheses square root of x squared minus x end root close parentheses squared end cell less than cell open parentheses square root of 2 close parentheses squared end cell row cell x squared minus x end cell less than cell open parentheses square root of 2 close parentheses squared end cell row cell x squared minus x end cell less than 2 row cell x squared minus x minus 2 end cell less than 0 row cell open parentheses x plus 1 close parentheses open parentheses x minus 2 close parentheses end cell less than 0 end table 
x equals negative 1 space atau space straight x equals 2 

negative 1 less than x less than 2  

Garis bilangan hasil irisan:



 

Jadi, himpunan penyelesaian dari Ptl adalah left curly bracket x vertical line minus 1 less than x less or equal than 0 space atau space 1 less or equal than x less than 2 right curly bracket.

Dengan demikian, jawaban yang tepat adalah D.

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