Question

Nilai Mutlak

1.) |3x+5| = |2x+20|
2.) |5/x-1| = 1/2
3.) Akar x^2-4x+4 = |2x+3| (pakai sifat |A|^2= (A)^2

Answer 1

Verified answer

Mapel : Matematika
Kelas : X SMA
Materi : Persamaan Mutlak

Pembahasan :
|3x + 5| = |2x + 20|
(3x + 5)² = (2x + 20)²
(3x + 5)² - (2x + 20)² = 0
(3x + 5 + 2x + 20)(3x + 5 - 2x - 20) = 0
(5x + 25)(x - 15) = 0
x = -5
x = 15

Hp : {-5 , 15}

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|5 / x - 1| = 1/2
|x - 1| = 2|5|
|x - 1| = 10
(x - 1)² = 10²
(x - 1)² - 10² = 0
(x - 1 + 10)(x - 1 - 10) = 0
(x + 9)(x - 11) = 0
x = -9
x = 11

Hp : {-9 , 11}

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√(x² - 4x + 4) = |2x + 3|
√(x - 2)² = |2x + 3|
x - 2 = |2x + 3|
(2x + 3)² = (x - 2)²
(2x + 3)² - (x - 2)² = 0
(2x + 3 + x - 2)(2x + 3 - x + 2) = 0
(3x + 1)(x + 5) = 0
x = -1/3
x = -5

Hp : {-5 , -1/3}