Roboguru

Diketahui  dan . Tentukan nilai  agar !

Diketahui f left parenthesis x right parenthesis equals fraction numerator 25 x minus 27 over denominator left parenthesis 2 x minus 3 right parenthesis left parenthesis 3 x minus 1 right parenthesis end fraction dan g left parenthesis x right parenthesis equals fraction numerator a over denominator 2 x minus 3 end fraction plus fraction numerator b over denominator 3 x minus 1 end fraction. Tentukan nilai a space dan space b agar f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis!

Jawaban:

Diketahui:

f left parenthesis x right parenthesis equals fraction numerator 25 x minus 27 over denominator left parenthesis 2 x minus 3 right parenthesis left parenthesis 3 x minus 1 right parenthesis end fraction dan g left parenthesis x right parenthesis equals fraction numerator a over denominator 2 x minus 3 end fraction plus fraction numerator b over denominator 3 x minus 1 end fraction

Mencari nilai a space dan space b:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell g open parentheses x close parentheses end cell row cell fraction numerator 25 x – 27 over denominator open parentheses 2 x – 3 close parentheses open parentheses 3 x – 1 close parentheses end fraction end cell equals cell fraction numerator a over denominator 2 x – 3 end fraction plus fraction numerator b over denominator 3 x – 1 end fraction end cell row cell fraction numerator 25 x – 27 over denominator open parentheses 2 x – 3 close parentheses open parentheses 3 x – 1 close parentheses end fraction end cell equals cell fraction numerator a open parentheses 3 x – 1 close parentheses over denominator open parentheses 2 x – 3 close parentheses open parentheses 3 x – 1 close parentheses end fraction plus fraction numerator b open parentheses 2 x – 3 close parentheses over denominator open parentheses 2 x – 3 close parentheses open parentheses 3 x – 1 close parentheses end fraction end cell row cell fraction numerator 25 x – 27 over denominator open parentheses 2 x – 3 close parentheses open parentheses 3 x – 1 close parentheses end fraction end cell equals cell fraction numerator a open parentheses 3 x – 1 close parentheses plus b open parentheses 2 x – 3 close parentheses over denominator open parentheses 2 x – 3 close parentheses open parentheses 3 x – 1 close parentheses end fraction end cell row cell 25 x – 27 end cell equals cell a open parentheses 3 x – 1 close parentheses plus b open parentheses 2 x – 3 close parentheses end cell row cell 25 x – 27 end cell equals cell 3 a x – a plus 2 b x – 3 b end cell row cell 25 x – 27 end cell equals cell open parentheses 3 a plus 2 b close parentheses x – open parentheses a plus 3 b close parentheses end cell end table 

Diperoleh sistem persamaan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a plus 2 b end cell equals cell 25 horizontal ellipsis open parentheses 1 close parentheses end cell row blank blank blank row cell a plus 3 b end cell equals 27 row a equals cell 27 – 3 b horizontal ellipsis open parentheses 2 close parentheses end cell end table 

Substitusikan persamaan (2) ke persamaan (1):

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a plus 2 b end cell equals 25 row cell 3 open parentheses 27 – 3 b close parentheses plus 2 b end cell equals 25 row cell 81 – 9 b plus 2 b end cell equals 25 row cell 81 – 25 end cell equals cell 9 b – 2 b end cell row 56 equals cell 7 b end cell row b equals cell 56 over 7 equals 8 end cell end table 

Substitusikan nilai b ke persamaan (2):

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 27 – 3 b end cell row blank equals cell 27 – 3 open parentheses 8 close parentheses end cell row blank equals cell 27 – 24 end cell row blank equals 3 end table 

Jadi, nilai a space dan space b yang memenuhi f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis adalah a equals 3 space dan space b equals 8.

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