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Matematika
harissaprullah
Pertanyaan
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1 Jawaban
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1. Jawaban arsetpopeye
f(x) = (x^2 - 2x + 5)/(x^2 + x)
asimtot tegak f(x)
x^2 + x = 0
x(x + 1) = 0
x = 0 atau x = -1
g(x) = (3x^2 - 4)/(x^2 + bx + c)
asimtot tegak g(x)
x^2 + bx + c = 0, b < 0
asimtot tegak g(x) berjarak 1 satuan dan 2 satuan dg salah satu asimtot tegak fungsi f
Ada beberapa kemungkinan:
1) berjarak 1 satuan dengan x = 0 => x = 1 dan x = -1
berjarak 2 satuan dengan x = 0 => x = 2 dan x = -2
(a) x = 1 dan x = 2 => (x - 1)(x - 2) = x^2 - 3x + 2 => memenuhi karena b < 0
(b) x = 1 dan x = -2 => (x - 1)(x + 2) = x^2 + x - 2 => tdk memenuhi krn b > 0
(c) x = -1 dan x = 2 => (x + 1)(x - 2) = x^2 - x - 2 => memenuhi krn b < 0
(d) x = -1 dan x = -2 => (x + 1)(x + 2) = x^2 + 3x + 2 => tdk memenuhi krn b > 0
2) berjarak 1 satuan dg x = -1 => x = 0 dan x = -2
berjarak 2 satuan dg x = -1 => x = 1 dan x = -3
(a) x = 0 dan x = 1 => x(x - 1) = x^2 - x => memenuhi krn b < 0
(b) x = 0 dan x = -3 => x(x + 3) = x^2 + 3x => tdk memenuhi krn b > 0
(c) x = -2 dan x = 1 => (x + 2)(x - 1) = x^2 + x - 2 => tdk memenuhi krn b > 0
(d) x = -2 dan x = -3 => (x + 2)(x + 3) = x^2 + 5x + 6 => tdk memenuhi krn b > 0
jadi yg memenuhi
1a) x^2 - 3x + 2 = 0 => b + c = -3 + 2 = -1
1c) x^2 - x - 2 = 0 => b + c = -1 - 2 = -3
2a) x^2 - x = 0 => b + c = -1 + 0 = -1