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Jika x1​ dan x2​, akar-akar 2x2−10x+4=0, nilai dari x12​+x22​−3x1​x2​=....

Pertanyaan

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

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

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

19

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Pertanyaan serupa

Diketahui x1​ dan x2​ adalah akar-akar persamaan kuadrat x2+6x+2=0. Nilai dari x12​+x22​−4x1​x2​ adalah ....

289

5.0

Jawaban terverifikasi

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