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Pertidaksamaan x 2 ​ ​ + 1 > 3 − x 2 ​ ​ terdevinisi untuk nilai x pada interval

Pertidaksamaan  terdevinisi untuk nilai  pada interval

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E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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nilai pada interval .

 nilai x pada interval x element of left square bracket 2 over 3 comma space 3 plus square root of 5 right parenthesis.

Pembahasan

Diketahui pertidaksamaan . Jabarkan pertidaksamaan ke dalam dua bentuk kemungkinan: Tentukan pada pada pertidaksamaan . Gunakan rumus ABC: Didapat ketaksamaan untuk dari adalah: Himpunannya: Gabungannya: Irisannya: Jadi,nilai pada interval .

Diketahui pertidaksamaan square root of 2 over x end root plus 1 greater than square root of 3 minus 2 over x end root.   

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 2 over x end root plus 1 end cell greater than cell square root of 3 minus 2 over x end root end cell row cell open parentheses square root of 2 over x end root plus 1 close parentheses squared end cell greater than cell open parentheses square root of 3 minus 2 over x end root close parentheses squared end cell row cell 2 over x plus 2 square root of 2 over x end root plus 1 end cell greater than cell 3 minus 2 over x end cell row cell 2 square root of 2 over x end root end cell greater than cell 3 minus 2 over x minus 2 over x minus 1 end cell row cell 2 square root of 2 over x end root end cell greater than cell 2 minus 4 over x end cell end table

Jabarkan pertidaksamaan ke dalam dua bentuk kemungkinan:

2 square root of 2 over x end root greater than 2 minus 4 over x comma space 2 minus 4 over x greater or equal than 0 2 square root of 2 over x end root greater than 2 minus 4 over x comma space 2 minus 4 over x less than 0 

Tentukan x pada pada pertidaksamaan 2 square root of 2 over x end root greater than 2 minus 4 over x.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 square root of 2 over x end root end cell equals cell 2 minus 4 over x end cell row cell open parentheses 2 square root of 2 over x end root close parentheses squared end cell equals cell open parentheses 2 minus 4 over x close parentheses squared end cell row cell 4 times 2 over x end cell equals cell 4 minus 16 over x plus 16 over x squared end cell row cell 8 x end cell equals cell 4 x squared minus 16 x plus 16 end cell row 0 equals cell 4 x squared minus 24 x plus 16 end cell row 0 equals cell x squared minus 6 x plus 4 end cell end table

Gunakan rumus ABC:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 12 end cell equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative open parentheses negative 6 close parentheses plus-or-minus square root of open parentheses negative 6 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses 4 close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 6 plus-or-minus square root of 36 minus 16 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 6 plus-or-minus square root of 20 over denominator 2 end fraction end cell row blank equals cell fraction numerator 6 plus-or-minus 2 square root of 5 over denominator 2 end fraction end cell row blank equals cell 3 plus-or-minus square root of 5 end cell end table

Didapat ketaksamaan untuk x dari 2 square root of 2 over x end root greater than 2 minus 4 over x comma space 2 minus 4 over x greater or equal than 0 space dan space 2 square root of 2 over x end root greater than 2 minus 4 over x comma space 2 minus 4 over x less than 0 adalah:

x element of open parentheses 3 minus square root of 5 comma space 3 plus square root of 5 close parentheses comma space x element of open parentheses negative infinity comma 0 close parentheses union left square bracket 2 comma plus infinity right parenthesis x element of straight real numbers comma space x element of open parentheses 0 comma 2 close parentheses

Himpunannya:

x element of left square bracket 2 comma space 3 plus square root of 5 right parenthesis x element of open parentheses 0 comma 2 close parentheses

Gabungannya:

x element of open parentheses 0 comma space 3 plus square root of 5 close parentheses comma space x element of left square bracket 2 over 3 comma space plus infinity right parenthesis

Irisannya:

x element of left square bracket 2 over 3 comma space 3 plus square root of 5 right parenthesis 

Jadi, nilai x pada interval x element of left square bracket 2 over 3 comma space 3 plus square root of 5 right parenthesis.

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