soal no 8 gimana caranya?
Matematika
sgboi
Pertanyaan
soal no 8 gimana caranya?
1 Jawaban
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1. Jawaban SadonoSukirno
misal alfa = a dan beta = b
a) I) a² - ab + b² = a² + b² - ab
= (a + b)² - 2ab - ab
= (a + b)² - 3ab
II)
dari persamaan kuadrat pertama
a + b = -2/1 = -2
a.b = m/1 = m
dari persamaan kuadrat kedua
a³.b³ = 512/1 = 512
(a.b)³ = 512
a.b = ³√512
a.b = 8
m = 8
a³ + b³ = -n/1 = -n
(a + b)³ - 3ab(a + b) = -n
(-2)³ - 3(8)(-2) = -n
-8 + 48 = -n
40 = -n
n = -40
b) persamaan kuadrat x² - (x1+x2)x + x1.x2 = 0
x1 + x2 = a / (a+b) + b/(a+b)
= (a+b) / (a+b)
= 1
x1.x2 = a / (a+b) × b(a+b)
= a.b / (a+b)²
= (-2/4) / (-1/4)²
= (-1/2) / (1/16)
= (-1/2) × (16/1)
= -8
x² - 1x + (-8) = 0
x² - x - 8 = 0