Jika jumlah kuadrat akar-akar real persamaan x2−2x−a=0 sama dengan jumlah kebalikan akar-akar persamaan x2−8x+(a−1)=0, maka nilai a adalah...

Pertanyaan

Jika jumlah kuadrat akar-akar real persamaan x squared minus 2 x minus a equals 0 sama dengan jumlah kebalikan akar-akar persamaan x squared minus 8 x plus left parenthesis a minus 1 right parenthesis equals 0, maka nilai a adalah...

  1. 2

  2. -3

  3. -1

  4. negative 1 half

  5. 3

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

Jumlah kuadrat akar-akar real persamaan x squared minus 2 x minus a. Misal akar-akarnya alpha space d a n space beta colon

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 x subscript 2  alpha squared plus beta squared equals left parenthesis alpha plus beta right parenthesis squared minus 2 alpha beta  space space space space space space space space space space space space equals open parentheses negative b over a close parentheses squared minus 2 open parentheses c over a close parentheses  space space space space space space space space space space space space equals 2 squared minus 2 left parenthesis negative a right parenthesis  space space space space space space space space space space space space equals 4 plus 2 a

Jumlah kebalikan akar-akar persamaan

x squared minus 8 x plus left parenthesis a minus 1 right parenthesis equals 0  1 over x subscript 1 plus 1 over x subscript 2 equals fraction numerator x subscript 1 plus x subscript 2 over denominator x subscript 1 x subscript 2 end fraction equals fraction numerator open parentheses negative begin display style b over a end style close parentheses over denominator open parentheses begin display style c over a end style close parentheses end fraction equals fraction numerator 8 over denominator a minus 1 end fraction

M a k a space rightwards arrow 4 plus 2 a equals fraction numerator 8 over denominator a minus 1 end fraction  left parenthesis 4 plus 2 a right parenthesis left parenthesis a minus 1 right parenthesis equals 8  2 a squared plus 2 a minus 12 equals 0  a squared plus a minus 6 equals 0  left parenthesis a plus 3 right parenthesis left parenthesis a minus 2 right parenthesis equals 0  a equals negative 3 space a t a u space a equals 2

S y a r a t space a k a r space r e a l space D greater than 0 space d a r i  x squared minus 2 x minus a equals 0  D greater than 0  b squared minus 4 a c greater than 0  4 minus 4 left parenthesis 1 right parenthesis left parenthesis negative a right parenthesis greater than 0  a greater than negative 1  M a k a space n i l a i space a space equals space 2

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Akar-akar persamaan x2+(a−1)x+2=0 adalah α dan β. Jika α=2β dan a > 0 maka nilai a = .....

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