nilai x yg memenuhi pertidaksamaan (x+2/x-1)²<_(kecil sama) 3(x+2/x-1)-2

Misal :
(x + 2) / (x - 1) = a

((x + 2)/(x - 1))² ≤ 3(x + 2)/(x - 1) - 2
a² - 3a + 2 ≤ 0
(a - 1)(a - 2) ≤ 0

Nilai a yg memenuhi :
1 ≤ a ≤ 2

•
a ≥ 1
(x + 2)/(x - 1) - (x - 1)/(x - 1) ≥ 0
3/(x - 1) ≥ 0
x > 1 ... (1)

••
a ≤ 2
(x + 2)/(x - 1) - 2(x - 1)/(x - 1) ≤ 0
(-x + 4)/(x - 1) ≤ 0

Pembuat nol
-x + 4 = 0 --> x = 4
x - 1 = 0 ---> x = 1

x yg memenuhi :
x < 1 atau x ≥ 4 ... (2)

▶
Nilai x yg memenuhi soal :
Irisan (1) dan (2)
x ≥ 4

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