Iklan

Iklan

Pertanyaan

Selesaikan SPLDV tersamar berikut. b. { 4 x 2 − 3 x ​ − 3 y 2 + 6 y ​ = − 1 2 1 ​ x 2 − 3 x ​ + y 2 + 6 y ​ = 3 ​

Selesaikan SPLDV tersamar berikut.

b.  

Iklan

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

penyelesaian dari setiap SPLDV tersebut adalah .

 penyelesaian dari setiap SPLDV tersebut adalah open parentheses fraction numerator 33 plus-or-minus square root of 2113 over denominator 22 end fraction comma space minus fraction numerator 33 plus-or-minus square root of 1714 over denominator 11 end fraction close parentheses.

Iklan

Pembahasan

Diketahui: Misalkan . Didapat: Mencari nilai dengan eliminasi : Substitusi ke persamaan pertama: Maka, Nilai : Nilai : Jadi,penyelesaian dari setiap SPLDV tersebut adalah .

Diketahui:

open curly brackets table attributes columnalign left end attributes row cell 4 square root of x squared minus 3 x end root minus 3 square root of y squared plus 6 y end root equals negative 1 end cell row cell 1 half square root of x squared minus 3 x end root plus square root of y squared plus 6 y end root equals 3 end cell end table close

Misalkan t equals square root of x squared minus 3 x end root comma space u equals square root of y squared plus 6 y end root. Didapat:

4 t minus 3 u equals negative 1 1 half t plus u equals 3  

Mencari nilai u dengan eliminasi t:

table row cell 4 t minus 3 u equals negative 1 end cell cell open vertical bar cross times 1 close vertical bar end cell cell 4 t minus 3 u equals negative 1 end cell row cell 1 half t plus u equals 3 end cell cell open vertical bar cross times 8 close vertical bar end cell cell 4 t plus 8 u equals 24 space space space minus end cell row blank blank cell negative 11 u equals negative 25 end cell row blank blank cell u equals 25 over 11 end cell end table       

Substitusi u ke persamaan pertama:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 t minus 3 u end cell equals cell negative 1 end cell row cell 4 t minus 3 open parentheses 25 over 11 close parentheses end cell equals cell negative 1 end cell row cell 4 t end cell equals cell negative 1 plus 3 times 25 over 11 end cell row cell 4 t end cell equals cell 64 over 11 end cell row t equals cell 16 over 11 end cell end table     

Maka,

Nilai x:

table attributes columnalign right center left columnspacing 0px end attributes row t equals cell square root of x squared minus 3 x end root end cell row cell 16 over 11 end cell equals cell square root of x squared minus 3 x end root end cell row cell 256 over 121 end cell equals cell x squared minus 3 x end cell row 56 equals cell 121 x squared minus 363 x end cell row 0 equals cell 121 x squared minus 363 x minus 256 end cell row cell x subscript 1 comma thin space 2 end subscript end cell equals cell fraction numerator negative open parentheses negative 363 close parentheses plus-or-minus square root of open parentheses negative 363 close parentheses squared minus 4 times thin space 121 open parentheses negative 256 close parentheses end root over denominator 2 times 121 end fraction end cell row cell x subscript 1 comma thin space 2 end subscript end cell equals cell fraction numerator negative open parentheses negative 363 close parentheses plus-or-minus thin space 11 square root of 2113 over denominator 2 times 121 end fraction end cell row blank equals cell fraction numerator 11 open parentheses 33 plus-or-minus square root of 2113 close parentheses over denominator 242 end fraction end cell row blank equals cell fraction numerator 33 plus-or-minus square root of 2113 over denominator 22 end fraction end cell end table   

Nilai y:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell square root of y squared plus 6 y end root end cell row cell 25 over 11 end cell equals cell square root of y squared plus 6 y end root end cell row cell 625 over 121 end cell equals cell y squared plus 6 y end cell row 625 equals cell 121 y squared plus 726 y end cell row 0 equals cell 121 y squared plus 726 y minus 625 end cell row cell y subscript 1 comma thin space 2 end subscript end cell equals cell fraction numerator negative 726 plus-or-minus square root of 726 squared minus 4 times 121 open parentheses negative 625 close parentheses end root over denominator 2 times 121 end fraction end cell row cell y subscript 1 comma thin space 2 end subscript end cell equals cell fraction numerator negative 726 plus-or-minus thin space 22 square root of 1714 over denominator 2 times 121 end fraction end cell row blank equals cell fraction numerator 22 open parentheses negative 33 plus square root of 1714 close parentheses over denominator 242 end fraction end cell row blank equals cell fraction numerator negative 33 plus-or-minus square root of 1714 over denominator 11 end fraction end cell end table  

Jadi, penyelesaian dari setiap SPLDV tersebut adalah open parentheses fraction numerator 33 plus-or-minus square root of 2113 over denominator 22 end fraction comma space minus fraction numerator 33 plus-or-minus square root of 1714 over denominator 11 end fraction close parentheses.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

76

Iklan

Iklan

Pertanyaan serupa

Selesaikan dan tuliskan HP-nya. b. { 6 1 ​ x + 2 1 ​ y = − 2 3 2 ​ x + 4 3 ​ y = 2 ​

1

0.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia