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

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

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Jumlah kuadrat akar-akar real persamaan Misal akar-akarnya Jumlah kebalikan akar-akar persamaan

Jumlah kuadrat akar-akar real persamaan Misal akar-akarnya

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