carilah nilai × yang memenuhi setiap persamaan nilai mutlak berikut. a.|4×+3|=7 b.|3×-8|=4 c.|5-2×|=11 d.|4+3×|=1 e.|4×-6|=10
Matematika
datobrajadaud
Pertanyaan
carilah nilai × yang memenuhi setiap persamaan nilai mutlak berikut. a.|4×+3|=7 b.|3×-8|=4 c.|5-2×|=11 d.|4+3×|=1 e.|4×-6|=10
1 Jawaban
-
1. Jawaban Ivanna24
a. |4x + 3| = 7 b. |3x - 8| = 4
(4x + 3)² = 7² (3x - 8)² = 4²
(4x + 3) (4x + 3) = 49 (3x - 8) (3x - 8) = 16
16x² + 12x + 12x + 9 = 49 9x² - 24x - 24x + 64 - 16 = 0
16x² + 24x + 9 - 49 = 0 9x² - 48x + 48 = 0
16x² + 24x - 40 = 0 Dibagi 3
Dibagi 8 3x² - 16x + 16x = 0
2x² + 3x - 5 = 0 (3x - 4) (x - 4) = 0
(2x + 5) (x - 1) = 0 3x - 4 = 0 atau x - 4 = 0
2x + 5 = 0 atau x - 1 = 0 3x = 4 x = 4
2x = -5 x = 1 x = 4/3
x = -5/2
c. |5 - 2x| = 11 d. |4 + 3x| = 1
(5 - 2x)² = 11² (4 + 3x)² = 1²
(5 - 2x) (5 - 2x) = 121 (4 + 3x) (4 + 3x) = 1
25 - 10x - 10x + 4x² -121 =0 16 + 12x + 12x + 9x² - 1= 0
4x² - 20x - 96 = 0 9x² + 24x + 15 = 0
Dibagi 4 Dibagi 3
x² - 5x - 24 = 0 3x² + 8x + 5 = 0
(x - 8) (x + 3) = 0 (3x + 5) (x + 1) = 0
x - 8 = 0 atau x + 3 = 0 3x + 5 = 0 atau x + 1 = 0
x = 8 x = -3 3x = -5 x = -1
x = -5/3
e. |4x - 6| = 10
(4x - 6)² = 10²
(4x - 6) (4x - 6) =100
16x² - 24x -24x + 36 - 100 = 0
16x² - 48x - 64 = 0
Dibagi 16
x² - 3x - 4 = 0
(x - 4) (x + 1) = 0
x - 4 = 0 atau x + 1 = 0
x = 4 x = -1