Question

Jika X₁ dan X₂ adalah akar-akar persamaan (5log(x + 3))² + 3 · ⁵log(x + 3) = ⁵log 1/25 maka |X₁ - X₂| = ....

Answer 1

Dengan ⁵log 1/25 = -2, maka:
(⁵log(x+3))² + 3.⁵log(x+3) = -2
(⁵log(x+3))² + 3.⁵log(x+3) + 2 = 0
(⁵log(x+3) + 1) (⁵log(x+3) + 2) = 0

Maka:
Solusi 1:
⁵log(x+3) = -1
⁵log(x+3) = ⁵log 1/5
x+3 = 1/5
x = 1/5 - 3
x = -14/5

Solusi 2:
⁵log(x+3) = -2
⁵log(x+3) = ⁵log 1/25
x+3 = 1/25
x = 1/25 - 3
x = -74/25

Yang membuat:
|x₁ - x₂| = |-14/5 - (-74/25)|
= |-14/5 + 74/25|
= |-70/25 + 74/25|
= 4/25

Answer 2

|x₁ - x₂| = |-14/5 - (-74/25)|
= |-14/5 + 74/25|
= |-70/25 + 74/25|
= 4/25