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Nilai  yang memenuhi pertidaksamaan  adalah ...

Pertanyaan

Nilai begin mathsize 14px style x end style yang memenuhi pertidaksamaan begin mathsize 14px style x squared open parentheses 2 x squared minus x close parentheses less than x squared open parentheses 2 x plus 5 close parentheses end style adalah ...

  1. begin mathsize 14px style 1 less than x less than 5 over 2 end style 

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

  3. begin mathsize 14px style x less than negative 1 end style atau begin mathsize 14px style x greater than 5 over 2 end style 

  4. begin mathsize 14px style x less than negative 1 end style atau begin mathsize 14px style 0 less than x less than 5 over 2 end style 

  5. begin mathsize 14px style negative 1 less than x less than 5 over 2 end style atau begin mathsize 14px style x not equal to 0 end style 

Pembahasan Soal:

Diketahui:

Fungsi pertidaksamaan begin mathsize 14px style x squared open parentheses 2 x squared minus x close parentheses less than x squared open parentheses 2 x plus 5 close parentheses end style.

Diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared left parenthesis 2 x squared minus x right parenthesis end cell less than cell x squared left parenthesis 2 x plus 5 right parenthesis end cell row cell 2 x to the power of 4 minus x cubed end cell less than cell 2 x cubed plus 5 x squared end cell row cell 2 x to the power of 4 minus x cubed minus 2 x cubed minus 5 x squared end cell less than 0 row cell 2 x to the power of 4 minus 3 x cubed minus 5 x squared end cell less than 0 row cell x squared open parentheses 2 x squared minus 3 x minus 5 close parentheses end cell less than 0 row cell x squared open parentheses 2 x open parentheses x plus 1 close parentheses minus 5 open parentheses x plus 1 close parentheses close parentheses end cell less than 0 row cell x squared open parentheses 2 x minus 5 close parentheses open parentheses x plus 1 close parentheses end cell less than 0 end table end style

begin mathsize 14px style right enclose table row cell x squared less than 0 end cell row cell x less than 0 end cell row space row space end table end enclose space right enclose table row cell 2 x minus 5 less than 0 end cell row cell 2 x less than 5 end cell row cell x less than 5 over 2 end cell end table end enclose space table row cell x plus 1 less than 0 end cell row cell x less than negative 1 end cell row space row space end table end style

Garis bilangannya adalah:

Uji titik diantara titik penyelesaian.

Titik begin mathsize 14px style x equals negative 2 rightwards arrow open parentheses negative 2 close parentheses squared open parentheses 2 open parentheses negative 2 close parentheses minus 5 close parentheses open parentheses negative 2 plus 1 close parentheses equals 4 open parentheses negative 9 close parentheses open parentheses negative 1 close parentheses equals 36 end style 

Titik begin mathsize 12px style x equals negative 1 half rightwards arrow open parentheses negative 1 half close parentheses squared open parentheses 2 open parentheses negative 1 half close parentheses minus 5 close parentheses open parentheses negative 1 half plus 1 close parentheses equals 1 fourth open parentheses negative 6 close parentheses open parentheses 1 half close parentheses equals negative 3 over 4 end style 

Titik begin mathsize 14px style x equals 0 rightwards arrow 0 squared open parentheses 2 open parentheses 0 close parentheses minus 5 close parentheses open parentheses 0 plus 1 close parentheses equals 0 end style

Titik begin mathsize 14px style x equals 1 rightwards arrow 1 squared open parentheses 2 open parentheses 1 close parentheses minus 5 close parentheses open parentheses 1 plus 1 close parentheses equals 1 open parentheses negative 3 close parentheses open parentheses 2 close parentheses equals negative 6 end style 

Titik begin mathsize 14px style x equals 3 rightwards arrow 3 squared open parentheses 2 open parentheses 3 close parentheses minus 5 close parentheses open parentheses 3 plus 1 close parentheses equals 9 open parentheses 1 close parentheses open parentheses 4 close parentheses equals 36 end style 

Karena pertidaksamaan begin mathsize 14px style less than 0 end style, maka himpunannya adalah hasil yang bernilai negatif.

 

Maka, nilai begin mathsize 14px style x end style yang memenuhi pertidaksamaan begin mathsize 14px style x squared open parentheses 2 x squared minus x close parentheses less than x squared open parentheses 2 x plus 5 close parentheses end style adalah begin mathsize 14px style negative 1 less than x less than 5 over 2 end style atau begin mathsize 14px style x not equal to 0 end style.

Jadi, jawaban yang tepat adalah E. 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

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