Carilah semua solusi (x,y) bilangan real untuk setiap persamaan kuadrat berikut dan lukiskan sketsa grafik penyelesaianya! {x2+y2=25x2−y2=7​

Pertanyaan

Carilah semua solusi left parenthesis x comma y right parenthesis bilangan real untuk setiap persamaan kuadrat berikut dan lukiskan sketsa grafik penyelesaianya!

open curly brackets table attributes columnalign left end attributes row cell x squared plus y squared equals 25 end cell row cell x squared minus y squared equals 7 end cell end table close

D. Wahyu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Diketahui:

x squared plus y squared equals 25 space... left parenthesis 1 right parenthesis x squared minus y squared equals 7 space minus y squared equals 7 minus x squared space left parenthesis Kedua space ruas space dikali space left parenthesis negative right parenthesis right parenthesis y squared equals negative 7 plus x squared space... left parenthesis 2 right parenthesis

Dengan mensubtitusikan persamaan (2) ke persamaan (1), sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 25 row cell x squared plus left parenthesis negative 7 plus x squared right parenthesis end cell equals 25 row cell 2 x squared end cell equals cell 25 plus 7 end cell row cell 2 x squared end cell equals 32 row cell x squared end cell equals cell 32 over 2 end cell row cell x squared end cell equals 16 row x equals cell plus-or-minus square root of 16 end cell row x equals cell plus-or-minus 4 end cell end table

Dimana, nilai x adalah 

x subscript 1 equals 4 space x subscript 2 equals negative 4

Mensubtitusikan x subscript 1 space space dan space space x subscript 2 ke persamaan (2) yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell y squared end cell equals cell negative 7 plus left parenthesis 4 right parenthesis squared end cell row cell space y squared end cell equals cell negative 7 plus 16 end cell row cell y squared end cell equals 9 row cell y squared end cell equals cell plus-or-minus square root of 9 end cell row y equals cell plus-or-minus 3 end cell row cell y subscript 1 end cell equals cell 3 space space space dan space space y subscript 2 equals negative 3 end cell end table

Jadi, solusi adalah (4,3, (4,-3), (-4,3) dan (-4,-3).

Grafik 

  • table attributes columnalign right center left columnspacing 0px end attributes row cell x blank squared minus y blank squared end cell equals 7 row cell space minus Sumbu space x comma space y end cell equals cell 0 colon end cell row cell space x blank squared minus 0 end cell equals cell 7 space end cell row cell x blank squared end cell equals cell 7 space end cell row x equals cell plus-or-minus square root of 7 end cell row cell space x blank subscript 1 end cell equals cell square root of 7 space comma space space x blank subscript 2 equals negative square root of 7 space end cell row cell space minus Sumbu space y comma space x end cell equals cell 0 colon space end cell row cell left parenthesis 0 to the power of right parenthesis 2 end exponent minus y squared end cell equals 7 row cell space minus y blank squared end cell equals cell 7 space end cell row y equals cell plus-or-minus square root of negative 7 end root space end cell row blank blank cell straight y space tidak space punya space solusi end cell row blank blank blank end table

Grafik

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