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Jika x subscript 1 space d a n space x subscript 2 merupakan akar-akar persamaan 4 x squared plus b x plus 4 equals 0 comma space b not equal to 0 comma space m a k a space 1 over x subscript 1 plus 1 over x subscript 2 equals 16 left parenthesis x subscript 1 cubed plus x subscript 2 cubed right parenthesis berlaku untuk b squared minus b equals....

  1. 0 atau 12

  2. 6 atau 12

  3. 20 atau 30

  4. 42 atau 56

  5. 72 atau 90

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

4 x squared plus b x plus 4 equals 0, jumlah dan hasil kali akar-akar persamaan kuadrat a x squared plus b x plus c equals 0

1. space x subscript 1 plus x subscript 2 equals negative b over a  2. space x subscript 1 times x subscript 2 equals c over a  3. space x subscript 1 squared plus x subscript 2 squared equals left parenthesis x subscript 1 plus x subscript 2 right parenthesis squared minus 2 x subscript 1 times 2 x subscript 2  x subscript 1 plus x subscript 2 equals negative b over a equals negative b over 4  x subscript 1 x subscript 2 equals c over a equals 4 over 4 equals 1  1 over x subscript 1 plus 1 over x subscript 2 equals 16 left parenthesis x subscript 1 cubed plus x subscript 2 cubed right parenthesis  fraction numerator x subscript 1 plus x subscript 2 over denominator x subscript 1 x subscript 2 end fraction equals 16 left parenthesis x subscript 1 squared plus x subscript 2 squared minus 1 right parenthesis left parenthesis negative b over 4 right parenthesis  fraction numerator negative begin display style b over 4 end style over denominator 1 end fraction equals 16 left parenthesis x subscript 1 squared plus x subscript 2 squared minus 1 right parenthesis open parentheses negative b over 4 close parentheses  1 equals 16 left parenthesis x subscript 1 squared plus x subscript 2 squared minus 1 right parenthesis  1 over 16 equals left parenthesis x subscript 1 plus x subscript 2 right parenthesis squared minus 2 x subscript 1 x subscript 2  1 over 16 equals open parentheses negative b over 4 close parentheses squared minus 2 left parenthesis 1 right parenthesis minus 1  1 over 16 equals b squared over 16 minus 3  1 equals b squared minus 48  b squared minus 49 equals 0  left parenthesis b minus 7 right parenthesis left parenthesis b plus 7 right parenthesis equals 0  b equals 7 comma space b equals negative 7  b equals 7 rightwards arrow b squared minus b equals 49 minus 7 equals 42  b equals 7 rightwards arrow b squared minus b equals 49 plus 7 equals 56

22

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Tentukan nilai dari jumlah dan hasil kali akar-akar persamaan kuadrat 3x2+8x+4=0.

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