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Jika x1​ dan x2​ adalah akar-akar persamaan kuadrat x2−2x+1=0. Tentukanlah: a. x1​+x2​  b. x1​⋅x2​  c. x12​+x22​  d. x12​⋅x2​+x22​⋅x1​  e. x1​x2​​+x2​x1​​

Pertanyaan

Jika x subscript 1 space dan space x subscript 2 adalah akar-akar persamaan kuadrat x squared minus 2 x plus 1 equals 0. Tentukanlah:

a. x subscript 1 plus x subscript 2 

b. x subscript 1 times x subscript 2 

c. x subscript 1 squared plus x subscript 2 squared 

d. x subscript 1 squared times x subscript 2 plus x subscript 2 squared times x subscript 1 

e. x subscript 2 over x subscript 1 plus x subscript 1 over x subscript 2 

D. Enty

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari x subscript 2 over x subscript 1 plus x subscript 1 over x subscript 2 adalah 2.

Pembahasan

Diketahui persamaan kuadrat x squared minus 2 x plus 1 equals 0.

a. Mencari hasil dari x subscript 1 plus x subscript 2:

x subscript 1 plus x subscript 2 equals negative b over a equals negative fraction numerator negative 2 over denominator 1 end fraction equals 2 

Jadi, hasil dari x subscript 1 plus x subscript 2 adalah 2.

b. Mencari hasil dari x subscript 1 times x subscript 2:

x subscript 1 times x subscript 2 equals c over a equals 1 over 1 equals 1  

Jadi, hasil dari x subscript 1 times x subscript 2 adalah 1.

c. Mencari hasil dari x subscript 1 squared plus x subscript 2 squared:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared end cell equals cell open parentheses x subscript 1 plus x subscript 2 close parentheses squared minus 2 x subscript 1 times x subscript 2 end cell row blank equals cell 2 squared minus 2 times 1 end cell row blank equals cell 4 minus 2 end cell row blank equals 2 end table   

Jadi, hasil dari x subscript 1 squared plus x subscript 2 squared adalah 2.

d. Mencari hasil dari x subscript 1 squared times x subscript 2 plus x subscript 2 squared times x subscript 1:

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

Jadi, hasil dari x subscript 1 squared times x subscript 2 plus x subscript 2 squared times x subscript 1 adalah 2.

e. Mencari hasil dari x subscript 2 over x subscript 1 plus x subscript 1 over x subscript 2:

   table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 2 over x subscript 1 plus x subscript 1 over x subscript 2 end cell equals cell fraction numerator x subscript 1 squared plus x subscript 2 squared over denominator x subscript 1 times x subscript 2 end fraction end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table   

Jadi, hasil dari x subscript 2 over x subscript 1 plus x subscript 1 over x subscript 2 adalah 2.

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