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Pertanyaan

Solve the following x dan y in terms of p dan q . { x y + pq = 2 ⋅ p x x 2 y 2 + p 2 q 2 = 2 ⋅ q 2 y 2 ​

Solve the following    in terms of  .

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D. Wahyu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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Pembahasan

Diketahui: Terlebih dahulu, subtitusikan persamaan (1) ke persamaan (2), sehingga Jadi, solusi dari sistem persamaan ini adalah

Diketahui:

table attributes columnalign left end attributes row cell x y plus p q equals 2 times p x end cell row cell p q equals 2 p x minus q y space... left parenthesis 1 right parenthesis end cell row blank row cell x squared y squared plus p squared q squared equals 2 times q squared y squared space end cell row cell left parenthesis x y right parenthesis squared plus left parenthesis p q right parenthesis squared equals 2 times left parenthesis q y right parenthesis squared space... left parenthesis 2 right parenthesis end cell end table

Terlebih dahulu, subtitusikan persamaan (1) ke persamaan (2), sehingga

left parenthesis x y right parenthesis squared plus left parenthesis 2 p x minus q y right parenthesis squared equals 2 times left parenthesis q y right parenthesis squared space left parenthesis x y right parenthesis squared plus 4 times left parenthesis p x right parenthesis squared minus 4 times p x squared y plus left parenthesis x y right parenthesis squared equals 2 times left parenthesis q y right parenthesis squared 4 times left parenthesis p x right parenthesis squared minus 4 times p x squared y space plus space 2 times left parenthesis x y right parenthesis squared minus 2 times left parenthesis q y right parenthesis squared equals 0 space left parenthesis Kedua space ruas space dibagi space 2 right parenthesis 2 times left parenthesis p x right parenthesis squared minus 2 times p x squared y space plus space left parenthesis x y right parenthesis squared minus left parenthesis q y right parenthesis squared equals 0 2 x squared times space left parenthesis p squared minus p y right parenthesis space plus y squared space left parenthesis x squared minus q squared right parenthesis equals 0  2 x squared times space left parenthesis p squared minus p y right parenthesis equals 0 left parenthesis p squared minus p y right parenthesis equals fraction numerator 0 over denominator 2 x squared end fraction left parenthesis p squared minus p y right parenthesis equals 0 up diagonal strike p squared space p end strike equals up diagonal strike p y p equals y  y squared space left parenthesis x squared minus q squared right parenthesis equals 0 left parenthesis x squared minus q squared right parenthesis equals 0 over y squared left parenthesis x squared minus q squared right parenthesis equals 0 left parenthesis x minus q right parenthesis left parenthesis x plus q right parenthesis equals 0 x minus q equals 0 x equals q x plus q equals 0 x equals negative q

Jadi, solusi dari sistem persamaan ini adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals q row cell x subscript 2 end cell equals cell negative q end cell row y equals p end table

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