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, , dan . maka nilai dari  = ...

Pertanyaan

fraction numerator x y over denominator x plus y end fraction equals 1 fourthfraction numerator x z over denominator x plus z end fraction equals 1 fifth, dan fraction numerator y z over denominator y plus z end fraction equals 1 over 7. maka nilai dari 1 over x plus 1 over y plus 1 over z = ...

Pembahasan Soal:

Diketahui : fraction numerator x y over denominator x plus y end fraction equals 1 fourthfraction numerator x z over denominator x plus z end fraction equals 1 fifth, dan fraction numerator y z over denominator y plus z end fraction equals 1 over 7

Jika fraction numerator x y over denominator x plus y end fraction equals 1 fourth maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x y over denominator x plus y end fraction end cell equals cell 1 fourth end cell row cell fraction numerator x plus y over denominator x y end fraction end cell equals 4 row cell 1 over x plus 1 over y end cell equals 4 end table 

Jika fraction numerator x z over denominator x plus z end fraction equals 1 fifth maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x z over denominator x plus z end fraction end cell equals cell 1 fifth end cell row cell fraction numerator x plus z over denominator x z end fraction end cell equals 5 row cell 1 over x plus 1 over z end cell equals 5 end table 

Jika fraction numerator y z over denominator y plus z end fraction equals 1 over 7 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y z over denominator y plus z end fraction end cell equals cell 1 over 7 end cell row cell fraction numerator y plus z over denominator y z end fraction end cell equals 7 row cell 1 over y plus 1 over z end cell equals 7 end table 

Eliminasikan persamaan pertama dan keduaspace 

stack attributes charalign center stackalign right end attributes row 1 over x plus 1 over y equals 4 end row row minus 1 over x plus 1 over z equals 5 end row horizontal line row 1 over y minus 1 over z equals negative 1 end row end stack 

Didapatkan 1 over y minus 1 over z equals negative 1 maka 1 over y equals negative 1 plus 1 over z 

Substitusikan nilai 1 over y ke persamaan 1 over y plus 1 over z equals 7 

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over y plus 1 over z end cell equals 7 row cell left parenthesis negative 1 plus 1 over z right parenthesis plus 1 over z end cell equals 7 row cell 2 over z end cell equals 8 row cell 1 over z end cell equals 4 end table 

Substitusikan nilai 1 over z ke persamaan  1 over x plus 1 over z equals 5 dan 1 over y plus 1 over z equals 7

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over x plus 1 over z end cell equals 5 row cell 1 over x plus left parenthesis 4 right parenthesis end cell equals 5 row cell 1 over x end cell equals 1 end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over y plus 1 over z end cell equals 7 row cell 1 over y plus left parenthesis 4 right parenthesis end cell equals 7 row cell 1 over y end cell equals 3 end table 

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 over x plus 1 over y plus 1 over z end cell equals cell 1 plus 3 plus 4 end cell row blank equals 8 end table 

Jadi, nilai dari 1 over x plus 1 over y plus 1 over z adalah 8.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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