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Jika  dan , akar-akar , nilai dari

Jika x subscript 1 dan x subscript 2, akar-akar 2 x squared minus 10 x plus 4 equals 0, nilai dari x subscript 1 squared plus x subscript 2 squared minus 3 x subscript 1 x subscript 2 equals....

  1. 20

  2. 15

  3. 10

  4. 5

  5. 1

Jawaban:

Bentuk umum persamaan kuadrat,

a x squared minus b x plus c equals 0

Maka

2 x squared minus 10 x plus 4 equals 0 rightwards arrow a equals 2 comma space b equals negative 10 comma space c equals 4.

Jika x subscript 1 dan x subscript 2 akar-akar persamaan kuadrat maka penjumlahan dan perkalian akar-akar memenuhi,

  • x subscript 1 plus x subscript 2 equals negative b over a  x subscript 1 plus x subscript 2 equals negative fraction numerator left parenthesis negative 10 right parenthesis over denominator 2 end fraction  x subscript 1 plus x subscript 2 equals 5
  • x subscript 1 x subscript 2 equals c over a  x subscript 1 x subscript 2 equals 4 over 2  x subscript 1 x subscript 2 equals 2

Jadi,

x subscript 1 squared plus x subscript 2 squared minus 3 x subscript 1 x subscript 2 equals left parenthesis x subscript 1 plus x subscript 2 right parenthesis squared minus 2 x subscript 1 x subscript 2 minus 3 x subscript 1 x subscript 2  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis x subscript 1 plus x subscript 2 right parenthesis squared minus 5 x subscript 1 x subscript 2  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals left parenthesis 5 right parenthesis squared minus 5 left parenthesis 2 right parenthesis  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 25 minus 10  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 15

0

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