(x³ - 3x - 2)/(x - 1) ≥ 2

Jawabnya adalah x ≤ -√5 , 0≤ x <1, x≥√5 Ingat (a-b-c)(d-e) = ad-bd-cd-ae+be+ce Jika f(x)/g(x) ≥ 0 , maka f(x).g(x) ≥ 0, syarat g(x)≠0 (x³ - 3x - 2)/(x - 1) ≥ 2 (x³ - 3x - 2)/(x - 1) - 2 ≥ 0 (x³ - 3x - 2)/(x - 1) -2(x-1)/(x-1)≥ 0 (x³ - 3x - 2)/(x - 1) - (2x-2)/(x-1) ≥ 0 (x³ - 3x - 2-2x+2)/(x - 1) ≥ 0 (x³-5x) /(x-1) ≥ 0 (x³ - 5x)(x - 1) ≥ 0, syarat x≠1 x(x²-5) (x-1) ≥ 0 x (x-√5)(x+√5)(x-1)≥ 0 x = 0 x = √5 x = -√5 x = 1 ++ |––––| ++ | –– | ++ ----•------•----•----•---- ..-√5......0....1...√5 x< -√5, misal x = -3 x (x-√5)(x+√5)(x-1) =-3(-3-√5)(-3+√5)(-3-1) = -3(9-3√5+3√5-5)(-4) = 12(4) = 48 , bernilai positif -√5 < x < 0, misal x = -1 x (x-√5)(x+√5)(x-1) = (-1)(-1-√5)(-1+√5)(-1-1) = (-1)(1-√5+√5-5)(-2) = 2(-4) = -8, bernilai negatif 0< x < 1, misal x = ½ x (x-√5)(x+√5)(x-1) = ½(½-√5)(½+√5)(½-1) = ½(¼-5)(-½) = (-¼)(-19/4) = 19/16, bernilai positif 1< x < √5, misal x = 2 x (x-√5)(x+√5)(x-1) = 2(2-√5)(2+√5)(2-1) = 2(4+2√5-2√5-5) (1) = (2)(-1) = -2, bernilai negatif x> √5, misal x = 3 x (x-√5)(x+√5)(x-1) = 3(3-√5)(3+√5)(3-1) = 3(9-5)(2) = 6(4) = 24, bernilai positif Karena x (x-√5)(x+√5)(x-1)≥ 0 Maka penyelesaiannya yang bernilai positif yaitu x ≤ -√5 , 0≤ x <1, x≥√5 Jadi jawabnya adalah x ≤ -√5 , 0≤ x <1, x≥√5