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Nilai x yang memenuhi pertidaksamaan x2+3x+2​ ≥2x2−x−3​, x∈R adalah....

Pertanyaan

Nilai begin mathsize 14px style x end style yang memenuhi pertidaksamaan begin mathsize 14px style square root of x squared plus 3 x plus 2 end root space greater or equal than square root of 2 x squared minus x minus 3 end root comma space x element of straight real numbers end style adalah....undefined 

  1. begin mathsize 14px style negative 2 less or equal than x less or equal than 5 end style 

  2. begin mathsize 14px style 3 over 2 less or equal than x less or equal than 5 end style 

  3. begin mathsize 14px style x less or equal than negative 1 space atau space x greater or equal than 5 end style 

  4. begin mathsize 14px style x less or equal than negative 2 space atau space x greater or equal than 3 over 2 end style 

  5. size 14px x size 14px less or equal than size 14px minus size 14px 2 size 14px space size 14px atau size 14px space size 14px x size 14px greater or equal than size 14px 5 

A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Kondisi jika kedua ruas bernilai positif :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of x squared plus 3 x plus 2 end root end cell greater or equal than cell square root of 2 x squared minus x minus 3 end root space space space space kuadratkan space kedua space ruas end cell row cell straight x squared plus 3 straight x plus 2 end cell greater or equal than cell 2 straight x squared minus straight x minus 3 end cell row 0 greater or equal than cell straight x squared minus 4 straight x minus 5 end cell row 0 greater or equal than cell open parentheses straight x minus 5 close parentheses open parentheses straight x plus 1 close parentheses end cell row blank blank blank end table end style 

Daerah penyelesaian (i)

Syarat dalam akar 1  :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus 3 x plus 2 end cell greater or equal than 0 row cell open parentheses x plus 1 close parentheses open parentheses x plus 2 close parentheses end cell greater or equal than 0 row blank blank blank end table end style 

Daerah penyelesaian akar 1

Syarat dalam akar 2

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x squared minus x minus 3 end cell greater or equal than 0 row cell open parentheses 2 x minus 3 close parentheses open parentheses x plus 1 close parentheses end cell greater or equal than 0 row blank blank blank end table end style 

Daerah penyelesaian akar 2

 

Daerah penyelesaian akhir :

Jadi jawaban yang tepat adalah B

 

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