Roboguru

Pertanyaan

Salah satu akar persamaan x cubed plus 5 x squared minus 9 x minus n equals 0 berlawanan dengan akar lainnya, maka nilai x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared adalah...space 

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared end cell equals 43 end table.

Pembahasan

Perhatikan penghitungan berikut!

Diketahui:

table row cell x cubed plus 5 x squared minus 9 x minus n equals 0 end cell cell rightwards arrow a equals 1 end cell row blank cell rightwards arrow b equals 5 end cell row blank cell rightwards arrow c equals negative 9 end cell row blank cell rightwards arrow d equals negative n end cell end table 

Berdasarkan rumus Vietta diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 plus x subscript 3 end cell equals cell negative b over a space horizontal ellipsis space left parenthesis straight i right parenthesis end cell row cell x subscript 1 x subscript 2 plus x subscript 2 x subscript 3 plus x subscript 1 x subscript 3 end cell equals cell c over a space horizontal ellipsis space left parenthesis ii right parenthesis end cell end table 

Salah satu akar berlawanan, sehingga dapat kita misalkan:

x subscript 1 equals negative x subscript 2 rightwards arrow x subscript 1 plus x subscript 2 equals 0 

  • Berdasarkan persamaan (i) diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 plus x subscript 3 end cell equals cell negative b over a end cell row cell 0 plus x subscript 3 end cell equals cell negative 5 over 1 end cell row cell x subscript 3 end cell equals cell negative 5 end cell end table 

  • Berdasarkan persamaan (ii) diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 x subscript 2 plus x subscript 2 x subscript 3 plus x subscript 1 x subscript 3 end cell equals cell c over a end cell row cell negative x subscript 2 x subscript 2 plus x subscript 2 open parentheses negative 5 close parentheses plus open parentheses negative x subscript 2 close parentheses open parentheses negative 5 close parentheses end cell equals cell fraction numerator negative 9 over denominator 1 end fraction end cell row cell negative x subscript 2 squared minus 5 x subscript 2 plus 5 x subscript 2 end cell equals cell negative 9 end cell row cell negative x subscript 2 squared end cell equals cell negative 9 end cell row cell x subscript 2 squared end cell equals 9 row cell x subscript 2 end cell equals cell plus-or-minus square root of 9 end cell row cell x subscript 2 end cell equals cell plus-or-minus 3 end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell untuk space x subscript 2 end cell equals 3 row cell x subscript 1 end cell equals cell negative x subscript 2 equals negative 3 end cell row blank blank blank row cell untuk space x subscript 2 end cell equals cell negative 3 end cell row cell x subscript 1 end cell equals cell negative x subscript 2 equals negative open parentheses negative 3 close parentheses equals 3 end cell end table 

Sehingga diperoleh:

 table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared end cell equals cell open parentheses 3 close parentheses squared plus open parentheses negative 3 close parentheses squared plus open parentheses negative 5 close parentheses squared equals 43 end cell row cell x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared end cell equals cell open parentheses negative 3 close parentheses squared plus open parentheses 3 close parentheses squared plus open parentheses negative 5 close parentheses squared equals 43 end cell end table    

Dengan demikian, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared end cell equals 43 end table.

49

0.0 (0 rating)

Pertanyaan serupa

Sepasang akar persamaan 2x3+px2−13x−6=0 adalah saling berkebalikan. Jumlah kedua akar berkebalikan tersebut adalah ....

26

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 Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia