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1 Jawaban
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1. Jawaban arsetpopeye
x^2 + 3x + 1 = 0
x1 + x2 = -b/a = -3/1 = -3
x1.x2 = c/a = 1/1 = 1
x2/x1 + x1/x2 = (x2^2 + x1^2)/(x1.x2)
= ((x1 + x2)^2 - 2x1.x2)/(x2.x2)
= ((-3)^2 - 2(1))/1
= (9 - 2)/1
= 7
Misal p = (2 + x2/x1) dan q = (2 + x1/x2)
p + q = (2 + x2/x1) + (2 + x1/x2)
= 4 + x2/x1 + x1/x2
= 4 + 7
= 11
p.q = (2 + x2/x1)(2 + x1/x2)
= 4 + 2 x1/x2 + 2 x2/x1 + 1
= 5 + 2(x1/x2 + x2/x1)
= 5 + 2(7)
= 5 + 14
= 19
Persamaan kuadrat baru
x^2 - (p + q)x + pq = 0
x^2 - 11x + 19 = 0