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Tentukan nilai , jika  dan  sebagai berikut :   dan

Pertanyaan

Tentukan nilai open vertical bar x y close vertical bar comma open vertical bar x close vertical bar comma open vertical bar y close vertical bar comma open vertical bar x plus y close vertical bar squared comma open vertical bar x minus y close vertical bar squared, jika x dan y sebagai berikut : 

x equals negative 6 dan y equals 4 

Pembahasan Soal:

Ingat definisi nilai mutlak berikut ini: 

open vertical bar x close vertical bar equals x space space space space comma space jika space x greater or equal than 0 open vertical bar x close vertical bar equals negative x space comma space jika space x less than 0 

Pada soal diberikan x equals negative 6 dan y equals 4 , dengan demikian nilai dari: 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x y close vertical bar end cell equals cell open vertical bar negative 6 times 4 close vertical bar equals open vertical bar negative 24 close vertical bar equals 24 end cell row blank blank blank row cell open vertical bar x close vertical bar end cell equals cell open vertical bar negative 6 close vertical bar equals 6 end cell row blank blank blank row cell open vertical bar y close vertical bar end cell equals cell open vertical bar 4 close vertical bar equals 4 end cell row blank blank blank row cell open vertical bar x plus y close vertical bar squared end cell equals cell open vertical bar negative 6 plus 4 close vertical bar squared equals open vertical bar negative 2 close vertical bar squared equals 2 squared equals 4 end cell row blank blank blank row cell open vertical bar x minus y close vertical bar squared end cell equals cell open vertical bar negative 6 minus 4 close vertical bar squared equals open vertical bar negative 10 close vertical bar squared equals 10 squared equals 100 end cell end table   

Jadi, nilai open vertical bar x y close vertical bar comma open vertical bar x close vertical bar comma open vertical bar y close vertical bar comma open vertical bar x plus y close vertical bar squared comma open vertical bar x minus y close vertical bar squared berturut-turut adalah 24 comma space 6 comma space 4 comma space 4 comma space 100.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Lestari

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 12 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan nilai  , jika  dan  sebagai berikut :   dan

Pembahasan Soal:

Ingat definisi nilai mutlak berikut ini: 

open vertical bar x close vertical bar equals x space space space space comma space jika space x greater or equal than 0 open vertical bar x close vertical bar equals negative x space comma space jika space x less than 0 

Pada soal diberikan x equals negative 8 dan y equals 2 , dengan demikian nilai dari: 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x y close vertical bar end cell equals cell open vertical bar negative 8 times 2 close vertical bar equals open vertical bar negative 16 close vertical bar equals 16 end cell row blank blank blank row cell open vertical bar x close vertical bar end cell equals cell open vertical bar negative 8 close vertical bar equals 8 end cell row blank blank blank row cell open vertical bar y close vertical bar end cell equals cell open vertical bar 2 close vertical bar equals 2 end cell row blank blank blank row cell open vertical bar x plus y close vertical bar squared end cell equals cell open vertical bar negative 8 plus 2 close vertical bar squared equals open vertical bar negative 6 close vertical bar squared equals 6 squared equals 36 end cell row blank blank blank row cell open vertical bar x minus y close vertical bar squared end cell equals cell open vertical bar negative 8 minus 2 close vertical bar squared equals open vertical bar negative 10 close vertical bar squared equals 10 squared equals 100 end cell end table 

Jadi, nilai  open vertical bar x y close vertical bar comma open vertical bar x close vertical bar comma open vertical bar y close vertical bar comma open vertical bar x plus y close vertical bar squared comma open vertical bar x minus y close vertical bar squared berturut-turut adalah 16 comma space 8 comma space 2 comma space 36 comma space 100.

0

Roboguru

Tentukan nilai  , jika  dan  sebagai berikut :   dan

Pembahasan Soal:

Ingat definisi nilai mutlak berikut ini: 

open vertical bar x close vertical bar equals x space space space space comma space jika space x greater or equal than 0 open vertical bar x close vertical bar equals negative x space comma space jika space x less than 0 

Pada soal diberikan x equals 4 dan y equals 5 , dengan demikian nilai dari: 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x y close vertical bar end cell equals cell open vertical bar 4 times 5 close vertical bar equals open vertical bar 20 close vertical bar equals 20 end cell row blank blank blank row cell open vertical bar x close vertical bar end cell equals cell open vertical bar 4 close vertical bar equals 4 end cell row blank blank blank row cell open vertical bar y close vertical bar end cell equals cell open vertical bar 5 close vertical bar equals 5 end cell row blank blank blank row cell open vertical bar x plus y close vertical bar squared end cell equals cell open vertical bar 4 plus 5 close vertical bar squared equals open vertical bar 9 close vertical bar squared equals 9 squared equals 81 end cell row blank blank blank row cell open vertical bar x minus y close vertical bar squared end cell equals cell open vertical bar 4 minus 5 close vertical bar squared equals open vertical bar negative 1 close vertical bar squared equals 1 squared equals 1 end cell end table 

Jadi, nilai  open vertical bar x y close vertical bar comma open vertical bar x close vertical bar comma open vertical bar y close vertical bar comma open vertical bar x plus y close vertical bar squared comma open vertical bar x minus y close vertical bar squared berturut-turut adalah 20 comma space 4 comma space 5 comma space 81 comma space 1.

0

Roboguru

Tentukan nilai , jika  dan  sebagai berikut :   dan

Pembahasan Soal:

Ingat definisi nilai mutlak berikut ini: 

open vertical bar x close vertical bar equals x space space space space comma space jika space x greater or equal than 0 open vertical bar x close vertical bar equals negative x space comma space jika space x less than 0 

Pada soal diberikan x equals 2 dan y equals negative 3 , dengan demikian nilai dari: 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x y close vertical bar end cell equals cell open vertical bar 2 times negative 3 close vertical bar equals open vertical bar negative 6 close vertical bar equals 6 end cell row blank blank blank row cell open vertical bar x close vertical bar end cell equals cell open vertical bar 2 close vertical bar equals 2 end cell row blank blank blank row cell open vertical bar y close vertical bar end cell equals cell open vertical bar negative 3 close vertical bar equals 3 end cell row blank blank blank row cell open vertical bar x plus y close vertical bar squared end cell equals cell open vertical bar 2 plus left parenthesis negative 3 right parenthesis close vertical bar squared equals open vertical bar negative 1 close vertical bar squared equals 1 squared equals 1 end cell row blank blank blank row cell open vertical bar x minus y close vertical bar squared end cell equals cell open vertical bar 2 minus left parenthesis negative 3 right parenthesis close vertical bar squared equals open vertical bar 2 plus 3 close vertical bar equals open vertical bar 5 close vertical bar squared equals 5 squared equals 25 end cell end table 

Jadi, nilai open vertical bar x y close vertical bar comma open vertical bar x close vertical bar comma open vertical bar y close vertical bar comma open vertical bar x plus y close vertical bar squared comma open vertical bar x minus y close vertical bar squared berturut-turut adalah 6 comma space 2 comma space 3 comma space 1 comma space 25.

0

Roboguru

Tentukan hasil dari: b.

Pembahasan Soal:

Nilai mutlak dari sebarang bilangan x element of R, yang dinotasikan dengan open vertical bar x close vertical bar, didefinisikan sebagai berikut.

open vertical bar x close vertical bar equals open curly brackets table attributes columnalign left end attributes row cell x space text jika end text space x greater or equal than 0 end cell row cell negative x space text jika end text space x less than 0 end cell end table close

Ingat sifat nilai mutlak:

open vertical bar a times b close vertical bar equals open vertical bar a close vertical bar open vertical bar b close vertical bar

open vertical bar a divided by b close vertical bar equals open vertical bar a close vertical bar divided by open vertical bar b close vertical bar

open vertical bar negative a close vertical bar equals open vertical bar a close vertical bar

Berdasarkan definisi tersebut, penyelesaian soal di atas, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar fraction numerator 5 over denominator negative 2 end fraction cross times 3 close vertical bar open vertical bar negative 24 close vertical bar open parentheses negative open vertical bar 1 over 6 close vertical bar close parentheses end cell row blank equals cell open vertical bar fraction numerator 5 over denominator negative 2 end fraction close vertical bar open vertical bar 3 close vertical bar open vertical bar negative 24 close vertical bar open parentheses negative fraction numerator open vertical bar 1 close vertical bar over denominator open vertical bar 6 close vertical bar end fraction close parentheses end cell row blank equals cell 5 over 2 cross times 3 cross times 24 cross times open parentheses negative 1 over 6 close parentheses end cell row blank equals cell negative 30 end cell end table

Dengan demikian, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 5 over denominator negative 2 end fraction cross times 3 close vertical bar open vertical bar negative 24 close vertical bar open parentheses negative open vertical bar 1 over 6 close vertical bar close parentheses end cell equals cell negative 30 end cell end table 

0

Roboguru

Tentukan hasil operasi nilai mutlak berikut.

Pembahasan Soal:

Berdasarkan definisi nilai mutlak (Tidak pernah bernilai negatif) dan menggunakan sifat-sifat nilai mutlak

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a close vertical bar open vertical bar b close vertical bar end cell equals cell open vertical bar a b close vertical bar end cell row cell open vertical bar a close vertical bar divided by open vertical bar b close vertical bar end cell equals cell open vertical bar a divided by b close vertical bar end cell end table

maka didapatkan

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 close vertical bar cross times open vertical bar negative 5 close vertical bar minus fraction numerator open vertical bar negative 12 close vertical bar over denominator open vertical bar 3 close vertical bar end fraction end cell equals cell open vertical bar 2 cross times open parentheses negative 5 close parentheses close vertical bar minus open vertical bar fraction numerator negative 12 over denominator 3 end fraction close vertical bar end cell row blank equals cell open vertical bar negative 10 close vertical bar minus open vertical bar negative 4 close vertical bar end cell row blank equals cell 10 minus 4 end cell row blank equals 6 end table

Dengan demikian, hasil operasi nilai mutlak tersebut adalah 6.

0

Roboguru

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