Roboguru

Tentukan nilai  dan  dari kesamaan berikut.

Pertanyaan

Tentukan nilai begin mathsize 14px style italic a end style dan begin mathsize 14px style b end style dari kesamaan berikut.

begin mathsize 14px style fraction numerator 2 x minus 3 over denominator x squared minus 4 end fraction equals fraction numerator a over denominator x plus 2 end fraction plus fraction numerator b over denominator x minus 2 end fraction end style    space 

Pembahasan Soal:

Untuk menyelesaikan persamaan berikut, kita harus menyamakan penyebut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 x minus 3 over denominator x squared minus 4 end fraction end cell equals cell fraction numerator a over denominator x plus 2 end fraction plus fraction numerator b over denominator x minus 2 end fraction end cell row cell fraction numerator 2 x minus 3 over denominator x squared minus 4 end fraction end cell equals cell fraction numerator a left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis end fraction plus fraction numerator b left parenthesis x plus 2 right parenthesis over denominator left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis end fraction end cell row cell fraction numerator 2 x minus 3 over denominator x squared minus 4 end fraction end cell equals cell fraction numerator a open parentheses x minus 2 close parentheses plus b left parenthesis x plus 2 right parenthesis over denominator x squared minus 4 end fraction end cell row cell fraction numerator 2 x minus 3 over denominator x squared minus 4 end fraction end cell equals cell fraction numerator open parentheses a x minus 2 a close parentheses plus left parenthesis b x plus 2 b right parenthesis over denominator x squared minus 4 end fraction end cell row cell fraction numerator 2 x minus 3 over denominator x squared minus 4 end fraction end cell equals cell fraction numerator a x plus b x minus 2 a plus 2 b over denominator x squared minus 4 end fraction end cell row cell 2 x minus 3 end cell equals cell a x plus b x minus 2 a plus 2 b end cell row cell 2 x minus 3 end cell equals cell x left parenthesis a plus b right parenthesis minus 2 left parenthesis a minus b right parenthesis end cell end table end style     

Diperoleh

begin mathsize 14px style 2 equals a plus b a equals 2 minus b end style 

begin mathsize 14px style 3 equals 2 left parenthesis a minus b right parenthesis end style 

Substitusikan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 3 equals cell 2 left parenthesis a minus b right parenthesis end cell row cell 3 over 2 end cell equals cell 2 minus b minus b end cell row cell 3 over 4 end cell equals cell negative 2 b end cell row b equals cell negative 3 over 8 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 2 minus b end cell row a equals cell 2 minus left parenthesis negative 3 over 8 right parenthesis equals 19 over 8 end cell end table end style  

Jadi, nilai begin mathsize 14px style italic a end style dan begin mathsize 14px style b end style yang memenuhi berturut-turut adalah begin mathsize 14px style 19 over 8 comma blank minus 3 over 8 end style          undefined 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved