Roboguru

5. Salah satu akar persamaan  berlawanan dengan akar lainnya, maka nilai  adalah...

Pertanyaan

5. 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 

Pembahasan Soal:

Perhatikan penghitungan berikut!

 x cubed plus 5 x squared minus 9 x minus n equals 0 a equals 1 semicolon space b equals 5 comma space c equals negative 9 comma space d equals negative n  Rumus space Vietta x subscript 1 plus x subscript 2 plus x subscript 3 equals negative b over a......... left parenthesis straight i right parenthesis x subscript 1 x subscript 2 plus x subscript 2 x subscript 3 plus x subscript 1 x subscript 3 equals c over a... left parenthesis ii right parenthesis x subscript 1 x subscript 2 x subscript 3 equals negative d over a............... left parenthesis iii right parenthesis Salah space satu space akar space berlawanan comma misal colon x subscript 1 equals negative x subscript 2 rightwards arrow x subscript 1 plus x subscript 2 equals 0 Berdasarkan space pers. left parenthesis straight i right parenthesis x subscript 1 plus x subscript 2 plus x subscript 3 equals negative b over a 0 plus x subscript 3 equals negative 5 over 1 x subscript 3 equals negative 5  Berdasarkan space pers. left parenthesis ii right parenthesis x subscript 1 x subscript 2 plus x subscript 2 x subscript 3 plus x subscript 1 x subscript 3 equals c over a minus 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 equals fraction numerator negative 9 over denominator 1 end fraction minus x subscript 2 squared minus 5 x subscript 2 plus 5 x subscript 2 equals negative 9 minus x subscript 2 squared equals negative 9 x subscript 2 squared equals 9 x subscript 2 equals plus-or-minus square root of 9 x subscript 2 equals plus-or-minus 3  untuk space x subscript 2 equals 3 x subscript 1 equals negative x subscript 2 equals negative 3  untuk space x subscript 2 equals negative 3 x subscript 1 equals negative x subscript 2 equals negative open parentheses negative 3 close parentheses equals 3  sehingga comma x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared equals open parentheses 3 close parentheses squared plus open parentheses negative 3 close parentheses squared plus open parentheses negative 5 close parentheses squared equals 43 x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared equals open parentheses negative 3 close parentheses squared plus open parentheses 3 close parentheses squared plus open parentheses negative 5 close parentheses squared equals 43    

Jadi, hasilnya adalah 43. space 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

Ruangguru

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

Ikuti Kami

©2021 Ruangguru. All Rights Reserved