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Nilai-nilai x yang memenuhi pertidaksarnaan x+2>10−x2​ adalah ...

Pertanyaan

Nilai-nilai x yang memenuhi pertidaksarnaan x plus 2 greater than square root of 10 minus x squared end root adalah ...

  1. negative square root of 10 less or equal than x less or equal than square root of 10 

  2. x less than negative 3 space atau space x greater than 1 

  3. 2 less or equal than x less or equal than square root of 10 

  4. 1 less than x less or equal than square root of 10 

  5. negative 3 less than x less or equal than square root of 10 

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.

Pertidaksamaan:

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 end cell greater than cell square root of 10 minus x squared end root end cell row cell square root of 10 minus x squared end root end cell less than cell x plus 2 end cell end table 

Syarat numerus:

table attributes columnalign right center left columnspacing 0px end attributes row cell 10 minus x squared end cell greater or equal than 0 row cell negative x squared plus 10 end cell greater or equal than cell thin space 0 end cell row cell x squared minus 10 end cell less or equal than 0 row cell open parentheses x minus square root of 10 close parentheses open parentheses x plus square root of 10 close parentheses end cell less or equal than 0 row blank blank blank end table 
x equals square root of 10 comma space x equals negative square root of 10 

negative square root of 10 less or equal than x less or equal than square root of 10  

Proses menghilangkan akar:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 10 minus x squared end root end cell less than cell x plus 2 end cell row cell negative open parentheses x minus 1 close parentheses open parentheses x plus 3 close parentheses end cell less than 0 row cell open parentheses negative open parentheses x minus 1 close parentheses open parentheses x plus 3 close parentheses close parentheses open parentheses negative 1 close parentheses end cell greater than cell 0 times open parentheses negative 1 close parentheses end cell row cell open parentheses x minus 1 close parentheses open parentheses x plus 3 close parentheses end cell greater than 0 end table 
 x equals 1 comma space x equals negative 3 

x less than negative 3 space thin space atau space x greater than 1 

Garis bilangan hasil irisan:



 

Jadi, penyelesaian dari Ptl adalah 1 less than x less or equal than square root of 10.

Dengan demikian, jawaban yang tepat adalah D.

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