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Jika dan   adalah akar-akar persamaan kuadrat , ma...

Jika X subscript 1 dan X subscript 2  adalah akar-akar persamaan kuadrat x squared minus 3 x plus 1, maka persamaan kuadrat akar-akarnya x subscript 1 plus 1 over x subscript 1 dan x subscript 2 plus 1 over x subscript 2 adalah....

  1. undefined

  2. x squared minus space 6 x minus 6 equals space 0

  3. undefined

  4. undefined

  5. x squared minus 6 x minus 9 equals 0

Jawaban:

Jika X subscript 1 dan X subscript 2  adalah akar-akar persamaan kuadrat X squared minus 3 x plus 1 equals 0  maka :

x subscript 1 plus x subscript 2 equals 3

x subscript 1. x subscript 2 equals 1

Maka,

x 2 minus open parentheses x subscript 1 plus 1 over x subscript 1 plus x subscript 2 plus 1 over x subscript 2 close parentheses x plus open parentheses x subscript 1 plus 1 over x subscript 1 close parentheses open parentheses x subscript 2 plus 1 over x subscript 2 close parentheses equals 0

x squared minus open parentheses x subscript 1 plus x subscript 2 plus fraction numerator x subscript 2 plus x subscript 1 over denominator x subscript 1 x subscript 2 end fraction close parentheses x plus open parentheses x subscript 1 x subscript 2 plus x subscript 1 over x subscript 2 plus x subscript 2 over x subscript 1 plus fraction numerator 1 over denominator x subscript 1 x subscript 2 end fraction close parentheses equals 0

x subscript 2 minus open parentheses x subscript 1 plus x subscript 2 plus fraction numerator x subscript 2 plus x subscript 1 over denominator x subscript 1 x subscript 2 end fraction close parentheses x plus open parentheses x subscript 1 x subscript 2 plus fraction numerator x subscript 1 squared plus x subscript 2 squared over denominator x subscript 1 x subscript 2 end fraction plus fraction numerator 1 over denominator x subscript 1 x subscript 2 end fraction close parentheses equals 0

x squared minus open parentheses x subscript 1 plus x subscript 2 plus fraction numerator x subscript 2 plus x subscript 1 over denominator x subscript 1 x subscript 2 end fraction close parentheses x plus open parentheses x subscript 1 x subscript 2 plus fraction numerator open parentheses x subscript 1 plus x subscript 2 close parentheses squared minus 2 x subscript 1 x subscript 2 over denominator x subscript 1 x subscript 2 end fraction plus fraction numerator 1 over denominator x subscript 1 x subscript 2 end fraction close parentheses equals 0

x squared minus open parentheses 3 plus 3 over 1 close parentheses x plus open parentheses 1 plus fraction numerator left parenthesis 3 right parenthesis squared minus 2 left parenthesis 1 right parenthesis over denominator left parenthesis 1 right parenthesis end fraction plus 1 half close parentheses equals 0

x squared minus 6 x plus 9 equals 0

Jawaban C

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