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Jika  dan , maka nilai  adalah ....

Pertanyaan

Jika straight x equals 2 straight p minus 4 straight q dan straight y equals negative straight p plus 2 straight q, maka nilai fraction numerator 2 straight x squared minus 3 xy plus straight y squared over denominator straight x squared minus straight y squared end fraction adalah ....

  1. 1 fifth 

  2. 1 third 

  3. 3

  4. 5

Pembahasan Soal:

Dengan cara substitusi nilai x dan y sehingga :

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 straight x squared minus 3 xy plus straight y squared over denominator straight x squared minus straight y squared end fraction end cell equals cell fraction numerator 2 left parenthesis 2 straight p minus 4 straight q right parenthesis squared minus 3 left parenthesis 2 straight p minus 4 straight q right parenthesis left parenthesis negative straight p plus 2 straight q right parenthesis plus left parenthesis negative straight p plus 2 straight q right parenthesis squared over denominator left parenthesis 2 straight p minus 4 straight q right parenthesis squared minus left parenthesis negative straight p plus 2 straight q right parenthesis squared end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 4 straight p squared minus 16 pq plus 16 straight q squared right parenthesis minus 3 left parenthesis negative 2 straight p squared plus 8 pq minus 8 straight q squared right parenthesis plus left parenthesis negative straight p plus 2 straight q right parenthesis squared over denominator 4 straight p squared minus 16 pq plus 16 straight q squared minus left parenthesis straight p squared minus 4 pq plus 4 straight q squared right parenthesis end fraction end cell row blank equals cell fraction numerator 8 straight p squared minus 32 pq plus 32 straight q squared plus 6 straight p squared minus 24 pq plus 24 straight q squared plus straight p squared minus 4 pq plus 4 straight q squared over denominator 4 straight p squared minus 16 pq plus 16 straight q squared minus straight p squared plus 4 pq minus 4 straight q squared end fraction end cell row blank equals cell fraction numerator 15 straight p squared minus 60 pq plus 60 straight q squared over denominator 3 straight p squared minus 12 pq plus 12 straight q squared end fraction end cell row blank equals cell fraction numerator 15 left parenthesis straight p squared minus 4 pq plus 4 straight q squared right parenthesis over denominator 3 left parenthesis straight p squared minus 4 pq plus 4 straight q squared right parenthesis end fraction end cell row blank equals cell 15 over 3 end cell row blank equals 5 end table    

Jadii, Jika straight x equals 2 straight p minus 4 straight q dan straight y equals negative straight p plus 2 straight q, maka nilai fraction numerator 2 straight x squared minus 3 xy plus straight y squared over denominator straight x squared minus straight y squared end fraction adalah 5.

Oleh karena itu, Jawaban yang benar adalah D

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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