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Tentukan himpunan penyelesaian dari setiap pertidaksamaan nilai mutlak di bawah ini. a. ∣∣​x2−2∣∣​​>​1​

Pertanyaan

Tentukan himpunan penyelesaian dari setiap pertidaksamaan nilai mutlak di bawah ini.

a. table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x squared minus 2 close vertical bar end cell greater than 1 end table 

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari pertidaksamaan table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x squared minus 2 close vertical bar end cell greater than 1 end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets right enclose x x less than negative square root of 3 space space atau space minus 1 less than x less than 1 space atau space x greater than square root of 3 close curly brackets end cell end table 

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x squared minus 2 close vertical bar end cell greater than 1 row cell x squared minus 2 end cell less than cell negative 1 space atau space x squared minus 2 greater than 1 end cell row cell x squared minus 2 plus 1 end cell less than cell 0 space atau space x squared minus 2 minus 1 greater than 0 end cell row cell x squared minus 1 end cell less than cell 0 space atau space x squared minus 3 greater than 0 end cell row cell left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis end cell less than cell 0 space atau space left parenthesis x plus square root of 3 right parenthesis left parenthesis x minus square root of 3 right parenthesis greater than 0 end cell row cell negative 1 end cell less than cell x less than 1 space atau space open parentheses x less than negative square root of 3 space atau space x greater than square root of 3 close parentheses end cell row x less than cell negative square root of 3 space space atau space minus 1 less than x less than 1 space atau space x greater than square root of 3 end cell end table

Jadi, himpunan penyelesaian dari pertidaksamaan table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x squared minus 2 close vertical bar end cell greater than 1 end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets right enclose x x less than negative square root of 3 space space atau space minus 1 less than x less than 1 space atau space x greater than square root of 3 close curly brackets end cell end table 

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