Persamaan kuadrat x2−3x+2=0 mempunyai akar-akar x1 dan x2. Persamaan kuadrat yang akar-akarnya x12+x22 dan x12+x22 adalah ...

Pertanyaan

Persamaan kuadrat $x^2-3x+2=0$ mempunyai akar-akar $x_1$ dan $x_2$ . Persamaan kuadrat yang akar-akarnya $x_1^2+x_2^2$ dan $\frac2{x_1}+\frac2{x_2}$ adalah ...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Persamaan kuadrat x squared minus 3 x plus 2 equals 0 dengan a equals 1 , b equals minus sign 3 , dan c equals 2 mempunyai akar-akar x subscript 1 dan x subscript 2 .

Untuk menyusun persamaan kuadrat baru, gunakan konsep jumlah dan hasil kali akar persamaan kuadrat.

Jumlah dan hasil kali akar-akar

Jumlah akar-akar

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell negative straight b over straight a end cell row blank equals cell negative fraction numerator negative 3 over denominator 1 end fraction end cell row blank equals 3 end table$

Hasil kali akar-akar

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 end cell equals cell straight c over straight a end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table

Jumlah dan hasil kali akar-akar baru x subscript 1 equals x subscript 1 squared plus x subscript 2 squared dan x subscript 2 equals 2 over x subscript 1 plus 2 over x subscript 2 .

Jumlah akar-akar baru

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell open parentheses x subscript 1 squared plus x subscript 2 squared close parentheses plus open parentheses 2 over x subscript 1 plus 2 over x subscript 2 close parentheses end cell row blank equals cell fraction numerator open parentheses x subscript 1 squared plus x subscript 2 squared close parentheses open parentheses x subscript 1 times x subscript 2 close parentheses over denominator x subscript 1 times x subscript 2 end fraction plus fraction numerator 2 x subscript 2 over denominator x subscript 1 times x subscript 2 end fraction plus fraction numerator 2 x subscript 1 over denominator x subscript 1 times x subscript 2 end fraction end cell row blank equals cell fraction numerator open parentheses x subscript 1 plus x subscript 2 close parentheses squared minus open parentheses 2 x subscript 1 times x subscript 2 close parentheses open parentheses x subscript 1 times x subscript 2 close parentheses over denominator x subscript 1 times x subscript 2 end fraction plus fraction numerator 2 open parentheses x subscript 1 plus x subscript 2 close parentheses over denominator x subscript 1 times x subscript 2 end fraction end cell row blank equals cell fraction numerator 3 squared minus down diagonal strike 2 open parentheses 2 close parentheses open parentheses 2 close parentheses over denominator down diagonal strike 2 end fraction plus fraction numerator down diagonal strike 2 open parentheses 3 close parentheses over denominator down diagonal strike 2 end fraction end cell row blank equals cell 9 minus 4 plus 3 end cell row blank equals 8 end table$

Hasil kali akar-akar baru

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 end cell equals cell open parentheses x subscript 1 squared plus x subscript 2 squared close parentheses open parentheses 2 over x subscript 1 plus 2 over x subscript 2 close parentheses end cell row blank equals cell open parentheses x subscript 1 squared plus x subscript 2 squared close parentheses open parentheses fraction numerator 2 x subscript 2 plus 2 x subscript 1 over denominator x subscript 1 times x subscript 2 end fraction close parentheses end cell row blank equals cell open parentheses open parentheses x subscript 1 plus x subscript 2 close parentheses squared minus open parentheses 2 x subscript 1 times x subscript 2 close parentheses close parentheses open parentheses fraction numerator 2 open parentheses x subscript 1 plus x subscript 2 close parentheses over denominator x subscript 1 times x subscript 2 end fraction close parentheses end cell row blank equals cell open parentheses 3 squared minus 2 open parentheses 2 close parentheses close parentheses open parentheses fraction numerator down diagonal strike 2 open parentheses 3 close parentheses over denominator down diagonal strike 2 end fraction close parentheses end cell row blank equals cell open parentheses 9 minus 4 close parentheses open parentheses 3 close parentheses end cell row blank equals cell 5 open parentheses 3 close parentheses end cell row blank equals 15 end table$

Persamaan kuadrat baru

Persamaan kuadrat baru yang akar-akarnya x subscript 1 squared plus x subscript 2 squared dan 2 over x subscript 1 plus 2 over x subscript 2 yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus open parentheses x subscript 1 plus x subscript 2 close parentheses x plus open parentheses x subscript 1 times x subscript 2 close parentheses end cell equals 0 row cell x squared minus 8 x plus 15 end cell equals 0 end table

Persamaan kuadrat yang akar-akarnya x subscript 1 squared plus x subscript 2 squared dan 2 over x subscript 1 plus 2 over x subscript 2 adalah x squared minus 8 x plus 15 equals 0 .

Oleh karena itu, jawaban yang benar adalah A.

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